If you're just joining, you're listening to Post Roe Testing the Law. My name is Conor Goodwin, and I'm an events associate with ProPublica. For those new to us, ProPublica is a nonprofit newsroom dedicated to investigative journalism. In the aftermath of the Supreme Court decision to overturn Roe v. Wade, the legal landscape has shifted rapidly, creating confusion among people seeking reproductive health care and medical providers. In this moment of uncertainty, ProPublica has convened a group of experts to survey the current landscape on abortion rights, dissect legal strategies that play on both sides, and answer your questions. If you'd like to submit a question at any point, you can do so by clicking the Q&A icon at the bottom of your screen and typing it there. We'll try to answer as many as we can, but if we don't get to yours, I encourage you to join our next Post Roe event in early October. And now, allow me to introduce our speakers. Carlos Chapman is an associate professor of law at Washington and Lee University. Her scholarship on commercial litigation examines the interplay of business entities, government, and individuals. Kim Muncherson is co-dean and professor of law at Rutgers Law School. Her award-winning scholarship focuses on reproductive justice, bioethics, health law, and family. Nicole Santa Cruz is a reporter for ProPublica Southwest Unit, where she investigates how inequalities impact marginalized communities. And our moderator today is ProPublica senior editor, Ziva Branstetter. I'll let Ziva take it from here. Thanks so much, Connor. And thank you all for joining us. We go, this is a really important conversation to be having, and I'm just thrilled that we have such an all-star panel to guide us through this. I want to set the table a little bit and ask the panel, you know, more than two months out from the overturning of Roe v. Wade. How have you all seen abortion bans enforced in general? Are there any notable trends? What is surprised you as far as sort of the fallout? So I'll start. And, you know, I would say that there's nothing particularly surprising about what has happened, right? The expectation of anybody who's been paying attention was there would be chaos, and that's 100% what we have seen. So on one hand we have states that had trigger laws, and the question was, do they go into effect immediately? Or, you know, some of them had lag times. So there were all of those questions that were being asked. Lots of questions about what these statutes actually mean, right? These are not statutes that were written by healthcare providers. They're written by people in state legislatures. And so they use language that's not necessarily medical language. And so what we now have are lots of healthcare providers who, one, don't know what the law is, right, from day to day, in part because there's already lots of litigation going on. But also, even if they read it, it doesn't necessarily make sense given the kind of work that they are doing. So we're absolutely seeing that. Clinic closures, which of course don't just mean people don't get access to abortion. It also means people don't get access to birth control and plan B and all sorts of things. And then I think what we're really, and obviously we've seen lots of issues with miscarriage management because of these new rules and how vague they are. So, you know, I think that what we are looking at right now, no matter what some people, no matter what some state legislators might be saying right now is 100% a feature and not a bug. Right. The goal here was to create a set of circumstances where people who are abortion providers would not be able to provide abortions. And that's either because there's a ban or it's because the law is so vague that they don't know how they can practice medicine anymore. So we're in a really bad state if you care deeply about women and pregnant people and access to your productive medicine. Fascinating. Thank you so much. And we did have a comment that there was a listener who wanted us to speak up. So I'm going to try and do that. You are perfect. And let's see, Nicole, I wanted you to summarize, if you can, the story that you would you had written for public I'm sure most of our hundreds of viewers here read it. But can you remind them what you what you uncovered and what was so unusual about this case. Yeah, thanks Eva. Basically, I found out about a lawsuit where a woman who had ended an unwanted pregnancy with abortion pills that she obtained at a Phoenix clinic. She ended up involved in a lawsuit over that decision. The next husband ended up suing the abortion clinic where she obtained the abortion, and he filed a wrongful death lawsuit against that clinic, which is kind of a. This is a civil suit that's kind of seen as an enforcement mechanism to enforce anti abortion laws. So the National Right to Life Committee has recently released model legislation regarding ways to enforce abortion ban. So this is just kind of one sliver of the law that we could be seeing more of now. Yeah, it's an interesting issue because it has all sorts of unintended consequences or maybe intended as you know some of you can discuss later on. Carlos, can you talk to us about this about the questions of personhood, you know what have you learned so far and where do you think things might be headed related to this issue. And one of the things I'm thinking about and of course Cole story in the case that she wrote about is that that is exactly where personhood bills go you and recognize this as a person, it would enable a father, including fathers who are abusers to pursue the pregnant woman after the fact and to use the court system as a form of abuse. In my opinion that's just the beginning.  What happens when you know a father wants to block a form of health care for the mother. There is no limit to what happens when you are forcing a court or a doctor, or any other medical provider to compare the personhood of the fetus to the mothers that are thinking about the best life, you know the best interest of the person who was pregnant. You know there, there are tax and other implications to this. We have the example of the woman who tried to drive through the SUV lane, because there were two people, because she was pregnant or HP link, because there are two people like pregnant. We have the state of Georgia that has declared you can claim the fetus on your taxes, as soon as you know you're pregnant because they have a personhood statute. And I think there's no limit to where this can go. The questions I have are, are we allowed to state by state definitions of personhood, and how does that impact citizenship. How does impact the census count. How does that impact the federal tax code and not just a state tax code. And I think these are things that people have not thought through. The point of a personhood bill is to ban abortion, not to change immigration, or not to change citizenship, or to change the tax code. But those are the consequences, including you know the horrible situation that Nicole wrote about in her article. And that brings up such an interesting point about, you know, the people who are most affected by, by this bio returning review weighted by these abortion bands that Kim and Carlos could you both talk a little bit about who are the people in the communities, most harshly impacted by abortion bands and are there ways to protect those who are most vulnerable in a in a world without row. You know, especially in these states where the restrictions are so, so tight. Yeah, I mean so you know one thing that we that we know is that women of color, particularly black women are overrepresented in the folks who get abortions in this country.  They hurt women who, as Carlos was suggesting women who are in abusive relationships who may want to terminate a pregnancy because having a child with your abuser links you to that person in a way that you might not want to. So there are lots of folks who are particularly vulnerable who are not going to have access to abortion. One thing that I should say just to be really fair is that, you know, row has been on a death spiral for a very long time and certainly since 1992, when the Supreme Court decided Planned Parenthood versus Casey so there are lots of women in this country who have had very limited access to abortion services for a long time. And so to create a world that has the kind of patchwork that we're looking at right now. What it means is that, if you have privilege, right if you have the money that allows you to travel. If you don't have to worry about taking time off of work if you don't have to worry about finding childcare if you don't have to worry about driving 500 miles and paying for a hotel. So in order to have an abortion you're going to be much more well positioned. My lights have decided I'm not moving enough. You're going to be much more well positioned to actually be able to exercise a right to terminate a pregnancy, then lots and lots of people will be. And so it's really the women who are most vulnerable already who are hurt the most by banning abortion. Right. And I wanted to follow that up and talk a little bit about the ways that women and people who can become pregnant are affected and get into the weeds a little bit and talk about whether the consequences are intended or unintended, the consequences. You know, we've seen these anecdotal stories of, you know, people who didn't want to continue the pregnancy but you know couldn't get care so can you talk a little bit about the things that concern you most that are happening on the ground. I think the big thing obviously is that because healthcare providers aren't sure what the rules are, they don't know how to proceed. And I, you know, as much as I love lawyers, I'm a law professor I'm a lawyer. If I'm in a hospital because I need care for a miscarriage, I don't really want them calling a bunch of lawyers and saying well what should we do now. Right. Well, somebody is bleeding, but if they're still a fetal heartbeat you can't actually terminate that pregnancy so depending upon where you are of course what jurisdiction you're in so you know that that is a consequence that on one hand is potentially unintended but I also think that is a reflection of the fact that a lot of folks who wrote these laws seem to know very little about pregnancy and seem to knew very little about, you know, women's bodies right I mean the number of women who miscarry very early in in their life is probably a lot larger than a lot of these folks imagine or listening to people say things like an ectopic pregnancy doesn't require an abortion which is just such a such a such a reflection of just biologically not understanding how any of this any of this works. So we have women who are suffering who should not be suffering. We have healthcare providers who are probably worried not just about criminal liability but also civil liability, so you think you're following the law but then somebody ends up in a bad position and you get get sued for that. The other thing that I think is really important to remember here is because we have all of these different statutes, the rules and the standards are different as well so for instance we have one state that says, if you are you are terminated pregnancy because there's an exception that allows you to perform an abortion. You should do so in a way that is most likely to lead to the birth of a lead to a successful birth, which is a very strange position to take here and potentially a position that actually creates more risk for the person who is pregnant. Obviously deeply deeply problematic so you know we were just in a place where we are, we are putting lots of folks at risk and we are requiring them to subject themselves to both physical and psychological harm, and because the laws don't don't make any sense and what and one more thing that I should say here, even the laws that do have exceptions so they might have a life exception. One of the things about row and Casey was that it required not only an exception to save the life of the pregnant person but also health. Health isn't in a lot of the statute so let's say that what your physician wants to do is preserve your fertility. That's not saving your life right but it's putting you in a position where you could later have potentially another child and the law isn't protecting that. So we're we're in a space where I think that we really have a lot of work to do one to make sure that legislators actually understand what they're doing when they pass these bills, and also to make sure that people get the care that they are that they are entitled to Right. So interesting so Carlos, I wanted to have you weigh on this and then Kim as well, sort of looking ahead to the future, you know there are states that are where they have clearly said that abortion is legal here we want to provide that you know within our own state laws, we want to allow people who can become pregnant to come here and receive those services. So how are you seeing these states preparing to deal with what could be an influx of patients from states with bands, and how can these, how are these states expanding their capacity of you all seen any evidence of that, and then sort of related to that. The audience has a question about any basis in law for a state prohibiting travel to another state for an abortion. So whoever wants to take all that on, but basically abortion. I'll take the travel question first. And just as Kavanaugh said he felt like travel could not be banned and I tend to agree unconstitutional ban people to cross state lines. But the problem would not be banned from crossing state lines, it would be the civil penalty for aiding someone to cross state lines that could end up being a de facto travel ban. I don't know that our current court or current civil courts would find those things unconstitutional. And I feel like the Texas law has that to where it's like you know if you aid someone in traveling across state lines, we're not going to block that person, we're going to block you for getting a plane ticket for providing an abortion fund. You know I've seen states that are providing abortions ramp up services and plan for the influx putting more planning for clinics on borders, for example. And the problem is, not every state that currently provides abortion or that thinks their approach state is even safe safe and I think about Michigan, for example, or Virginia. I'm in Virginia now and they're planning a special session starting tomorrow, specifically to debate a person to bill and to ban abortion whereas Virginia is the only kind of bright spot, and a mass of states that have total bands or almost near to So, you know, the idea of safety and safe states to me is very tenuous. I just don't. I think that states definitely want to provide and want to be have their doors open, but I could see, you know these penalties being a problem. The other thing I've been thinking about though is the availability of Medicaid medical abortions by mail. And getting the prescription by prescriptions by mail. And I have been contemplating whether there's a federal preemption issue there. Because the FDA has defined that these, these medications are safe, that they can be shipped by telemedicine. They are prescribed for other uses and we've I've seen a lot of stories about women who are not getting like their medication for rheumatoid arthritis, other treatments because of fear that it could be an abortive kit. And I think that that kind of FDA battle, maybe a way that we can win some ground. Yes, it's very interesting because, you know, can states banned people from using things in the mail, you know. So it really sets up a federal state tension there that is going to need to play out in the courts or be tested. Follow up question from the audience what if a pregnant person is visiting a state on business or a vacation and needs care like, I mean, again, what restrictions would exist there. I mean, if you're if you're in a state that bands if you go for vacation in a state that bans abortion and you find yourself meeting an abortion, you might be in trouble right I mean so part of the part of the battle that's going on right now between the feds and the state is what Mtala means so Mtala is a statute that was passed many years ago, basically to keep hospitals from dumping patients right so you didn't want a patient to show up in an emergency. And the hospital says oh wait you don't have insurance let's go like put you on the street and then hope somebody else will deal with you. And so that you know the federal government came out and said listen if somebody needs abortion care under Mtala, then states are or healthcare providers are required to provide that care. And of course now we have two different decisions from two different courts federal courts already coming down on different sides of that issue right whether the federal government can tell a state that your abortion ban cannot be will not be enforced. If it is in violation of Mtala. And so one of the other things that I think is important of course is that once you have a circuit split so you know, Idaho says one thing Texas says something else, or, you know, whoever that that then winds its way back up to this US Supreme Court, which frankly I'm not particularly interested in seeing the US Supreme Court decide any more abortion cases, any time in the near future so that's really going to be playing playing itself out. And I wanted to add though and I think this goes to what Carlos was saying particularly about medication abortion. For a very, very long time it was a sort of basic tenant of the anti choice movement, you don't punish women, women, right, don't punish the people who are getting abortions, you punish the people who are providing abortions. It's such a different world now and one hand medication abortion is fantastic because it can be self managed and it can be done safely, and you can order the pills and they can come to your house. But because of that, I think one of the things that we are going to see is state saying alright we can't go after the doctors anymore, right because there are people who are performing their own abortions, safely, right which you, again, very safe to do so with women. So we're going to just have to start punishing those those women. And we're going to punish them by doing things like if you show up at the hospital and they think that you've used abortion pills, right then some, you know, a nurse or a doctor says well I guess I should call the police because I think you may have had an illegal abortion, you know so the consequences there are really significant potentially. And that's one of the things I'm really concerned about that the criminalization of pregnancy is simply going to expand and we know in this country that when pregnancy gets criminalized that that burden falls most on women of color and poor women. I mean, I, you know, speaking of that what the federal government has done can do and Tala is when one thing that they that the federal government has tried to invoke has the response from the federal government been adequate. There were a lot of criticism early after Ravi way was ever turned to the other Biden administration. I'm not doing enough. There have been some speeches but like, doesn't seem like a lot of action. There are options are fairly limited so what have the feds done to help and what the federal government done to help and what more do you all are experts think that the federal government should be doing. I can start on that one. You know I think, you know, the federal preemption issue and the fact that the federal has federal government has land is something that's not been exploited enough. Right, the federal government has hospitals. The federal government has lands that are federal lands. And I do not understand why we are not pushing state laws and performing abortions in states where there are bands on federal property and putting the federal sovereignty issue. And that's just one thing that I think could be happening. I don't quite understand. And I guess, you know, the counter argument to that is behind well in a lot of states they're civil. And there are several penalties for the doctors right so you know if a state has a civil penalty for a doctor performing an abortion period. And you're just putting a doctor in their license that risk, but I know abortion providers personally who would be willing to take that risk and be the test case. And so it doesn't it doesn't take many right it only takes a couple of places. Of course this issue. That's very interesting. You know, I'm based here in Oklahoma and there has been some discussion about native land and could, you know, you can't use federal funds but could you use private funds and there's been some reporting around this. So it's complicated but the tribes, you know, don't want to really wait are not eager to wait into that is what my reading of this is. audience question do we anticipate more federal challenges like we saw in in Idaho. And if, if you guys don't want to weigh in on this just let me know but. Oh this is, I mean, we're going to be litigating the idea that what the Supreme Court did was sort of take abortion off the table as an issue is just laughable. We're going to be litigating all so many issues, going forward, whether it's the preemption issue with federal versus state, whether it's trying to get clarity on what some of these laws are actually demanding, whether it's making decisions about what state can actually declare an embryo to be a person and what that means and how it plays itself out. You know, the big winners here are lawyers, frankly, because we're going to have a lot of work to do. Well, and, you know, Nicole's story pointed this out that there are issues involving, you know, who can decide, you know, fathers, rapists people who are sort of now think they have a stake in in deciding the fate of, you know, a woman's pregnancy. So it's very interesting to see all of these legal issues coming up and and sort of multiplying. Carlos, a lot of people talked about the nation of forced birth.  If you accept that as a, you know, that that is what's happening. How should they or should they be compensated. We've been looking into this and, you know, if the state wants to build a highway past your house and tear it down. They have to compensate you under something we call takings, right, they have to give you just competition for your for the for the taking of your property. You know, if the state is forcing to carry a child to term and to raise it. They should be compensating you for the taking of your body. And, you know, the question is how much and like what is just and where does it end in my my opinion. You know, you would at least think, you know, the medical expenses, the lost work, the cost of childbirth, the wear and tear on your body, you know, I'm 43 and if someone forced me to carry a child I didn't want to literally kill it could kill me right like it really good. I didn't want to compensate for that.  I did not intend to have you know a recent Wall Street Journal article said it is $300,000 on average to raise a child from zero to 18. And we are imposing a $300,000 burden on pregnant persons every time we force them to carry a child to term and bring that life into the world. And I personally think an abortion ban have a fiscal note that is, here's the cost of health care. Here's the cost of replacing losses. We know that women earn less over their lifetime, simply because they give, and when they give birth. How do we make up for that wage gap for the rest of your life. If you are forced to carry a child to term. I have a reader question of your question about abortion pills and do they just prevent pregnancy or what are they actually doing and just for those out there that it's actually to medication abortion is to two drugs. One is action and progesterone, which is essential to maintain pregnancy and then there's a second drug that has to be taken within 48 hours to complete the expulsion of the fertilized egg so just want to, you know, deliver those facts. Can I add something there though because I think this is actually a really important point. One of the other things that we're going to watch happen is that folks who are anti abortion are also sort of redefining what is an abortion. So, yes, medication abortion is an abortion right is it is keeping you from it is terminating a pregnancy plan B, which is contraception technically keeps you from becoming pregnant. And yet we've already seen so there was a case many years ago, the hobby lobby case that was decided and it was about the Affordable Care Act and whether employers could be required to provide birth control. And one of the things that hobby lobby said was, well we don't want to even allow people to get plan B we don't even want to allow people to get morning after pills. Because as far as we're concerned, anything that has the potential of keeping a fertilized egg from implanting is an abortion. So if we're going to then start expanding what it means for there to be an abortion, then you need to start being worried about your contraception. So we're being worried about a lot of things that normally we would have said this is totally irrelevant in this context so you know the Pandora's box that has been opened here is is much more substantial than just, can I terminate a pregnancy or not terminate a pregnancy. Great point. I wanted to build on I wanted to build on Kim's point and that, you know, when concern about the loss of certain birth control is not just because of the loss of privacy is because of how we are interpreting abortion so there are two ways in which birth control can fall. And then if we don't extend the falling the road to be overturning other cases that dealt with with birth control. It's the points that Kim made. So I think it's important to understand that the implications of this decision are very very broad fast. Right. And I just want to share the audience we are getting to the q amp a portion where we're going to be addressing many more questions from you. So, let's see. I think it's important to know that this is sort of the beginning, and not the end, like, we're just starting down a path. And so I wondered if you all had any, not not predictions but concerns or thoughts about big themes that are going to be developing in the next year to three if you know barring any major change in this really I think that there are a lot of surprises to come, frankly, for people I mean one is what Carlos was already alluding to which is, you know that. You know they were just salita was very careful in the opinion here to say, you know this is just about abortion it's just, it's really not about anything else, don't worry about anything else and yet the entire way the argument is constructed the opinion is essentially, you know the that the Constitution doesn't protect a right to privacy because the word privacy doesn't appear in the Constitution, well neither does woman neither does baby neither does you know a whole lot of things.  All of those are constitutionally protected because of privacy. Right, so one of the things that I think we really need to keep an eye on is sort of what are the next dominoes to fall. And because as you say row was a beginning row row was not an end it was an opportunity to one engage in a decades long campaign to build a Supreme Court that is now a very conservative Supreme Court and so there are so many issues that are going to come before that court where the impact will be much broader than you know whether you stay pregnant or or decide to terminate a pregnancy. I wanted to talk about some more legal questions. Carlos, are there any cases working their way through the courts that could end up at the Supreme Court that would give the justices. The opportunity to declare that a fetus to be a person with constitutional rights or any other cases that are sort of precedent setting in your mind potentially. So I've only been. I've only been focused on the person in cases and so far we don't have a specific case that I think would declare a fetus as a person but I want to reiterate what Kim said earlier about this current Supreme Court. I mean that they don't don't do that kind of as dictated to another case.  And, and we have seen the court before just rule on an issue that isn't in briefing or rule on an issue as a part of a bill. I don't want to to say no outright I want to qualify law professor answer of there aren't any directly but that doesn't mean that one won't make it to Supreme Court you won't have fetuses to third person. Great. So one of rose weaknesses was the standard of viability which can change over time as relevant sciences advance. So row in other words inflicted an unpredictable standard on people. Some would say, so should future abortion rights whether statutory or otherwise avoid the language of viability and in your, in your mind. And if so what do we replace that with. That's that that's an easy question. And so really it was Planned Parenthood versus Casey that really drill down on viability right because row gave us the three trimesters and it was much more protective of abortion rights and Planned Parenthood and viability. One of the long standing critiques of Planned Parenthood versus Casey was viability is is a shifting line, right, and for, for the better, it is a shifting line because science and medicine improved so I think that we're all we were always going to be comfortable if we were focused on the question of viability, as opposed to being focused on the question of equality of bodily integrity of medical decision making, and of privacy. And so, because we went in a particular direction, I think that sort of allowed us to kind of fall off a cliff. Whereas and there's lots of, you know, people who've written about this there were amicus briefs in, in, in the, in the dobs case about the idea that really what the conversation that we should be having when it comes to abortion and abortion rights is a conversation about equality sex equality, as opposed to having this conversation about, you know, what is a fetus and what is it a person, etc etc because at the, at the end of the day, whatever you think about what a fetus is or isn't no no one else in this country is told, we're in a way, rights to your body in order to benefit somebody else. Right, so if if I'm a parent and I have a child who needs a kidney and I'm a perfect match. The state can't force me to give up my kidney the state can't force me to even give blood to my kid. And yet in this context we're willing to say but you're in this context, your body is something that we can construct conscript for state purposes. Another, these are all reader questions at this point I mean the viewer questions at this point. So, another really interesting you talked about the hobby lobby case and, and this is sort of an outgrowth of that. What about the approach of demanding religious freedom to obtain an abortion, some religious groups include as a tenant that life does not begin until birth. And that spring court seems tilted pretty dramatically toward religious freedom. So it seems like an interesting way to turn that philosophy on its head what are the chances of such claims prevailing. Probably not good. I can, I can start on that one I think that when we, we have to acknowledge that when we say religious freedom in this country we tend to mean one religion in one religious perspective. And I think that those challenges will just reinforce that. I think that, you know, it's, it's like, well, we're only going to honor the religion that preserves line up the one that doesn't, or some kind of other work around to get around it but even the way hobby lobby decision is written, in my opinion. You know, it's a, I view that as a corporate person had decision, it's about, you know, whether a company should be able to make their employees or ban their employees from having access to certain health care. And we look at the religion of the founders and the like, it's our it's it's bad law and it's a bad, it's bad business law to start with, but we use religion to make bad business law. And I think it just doesn't stop there. Right. It, like we will make more bad law in the name of protecting one religion, not all. I was interested in Nicole and on your perspective, the story that she wrote is that an isolated case or are you seeing more cases like that, or is it too early to tell. At this point it's an isolated case. And as far as I know we haven't seen anything else like it. But I think it's still too early to tell kind of how much this is going to catch on, and sort of the civil actions that people will start taking. Great. And before this concludes Connor, if you can drop a just a general tip, a public tip line in the in the chat for people who, if you have story suggestions or questions or information that you think that our reporters who are working on this issue and Nicole and others need to know please, please reach out to us. Let's see. One of the questions that the viewers had is where do things stand with accepting with talked about this song but with accessing the abortion medication online there are I know European groups that I saw a story about people in Mexico they're sort of offshore operations that are trying to you know provide people who are pregnant with this medication. So where do things stand with the access to those medications. These are legal drugs, right, and their pills that are sold legally and they're sold not just for abortion purposes but for other purposes as well so you know states are states that want to ban abortion are obviously trying to figure out how wide a net. So whether it is cause was saying, you know before whether it's about, you know, punishing somebody, not saying you can't travel but punishing you when you come back from traveling. You know those are the kinds of things that states are going to start trying to do, and it creates another opportunity for the federal government to step in and say, you know you're overstepping your bounds here. And that's, that is another piece of litigation that I, I expect that we will see. The other thing to say about medication abortion though is that it's, it's, it's hard to know, right, I mean that's the reason why where we are now is really different from where we were before Roe versus Wade. You know, unless unless you show up at a hospital and somebody gets you to admit that you actually took abortion pills, it's going to be pretty hard to target people.  But just to say that it's pretty easy in some cases to get around the laws in your particular state so we'll see how that plays itself out and it goes back to what I said before. What about states starting to punish women as opposed to punish providers. We have some questions from healthcare providers who are listening today. One of them asks says I work in the meetings and hospitality industry. We're trying to understand the implications in trigger law states for a pregnant person from another state seeking emergency treatment aside from being turned away what legal issues. And I think one of you touched on this earlier. The laws of that state prevail right if you're in Louisiana or Mississippi or Oklahoma like that's that's the law you're operating on. So how fast can you get home. Right. What is the obligation of doctors is a healthcare provider asking the obligation of doctors to treat their patients according to standards of care, despite their own legal jeopardy. So I do bioethics as well. And you know and I think that the real the real question here and like Carlos I know a number of people who are abortion providers. And these are folks who are deeply committed to the work that they do, and they recognize how important it is for the patients for whom they are providing healthcare. And so there are definitely those who will say my obligation to my patient has to prevail over, you know whatever this particular rule is particularly rules that are vague and a number of these statutes are quite vague in the ways that they that they are articulated I think we will definitely definitely see healthcare providers who say, I have professional obligations and I will meet those professional obligations, and I will take the consequences that flow from that and there are others who will say, I'm not willing to lose my license to practice medicine which I think is 100% understandable. People who say I'm not willing to lose my freedom right I'm not going to go to prison. Again 100% understandable, but the folks who I know who do this work are so deeply committed to it and see it not just as a professional act but also as about equality and about compassion. And so I think a lot of them are going to be willing to put themselves at risk in order to provide the care that's appropriate care for their patients. I want to add something to that point I think the risk is not really for women who are seeing abortions as we've seen in all the press stories about women who are having miscarriages. The risk is for a woman who has a wanted pregnancy, an intended pregnancy and in the medical emergency, because it's that those doctors in the hospital who don't view themselves as abortion providers who seem to be making the difficult ethical decisions and in a hospital setting. They may not have a choice, they may not be able to, to provide the care until some higher up authorizes it. I think there's a false narrative that there's two, two situations here, one that wants to get rid of pregnancy, one wants to keep it there's all kinds of situations in the middle where people want to continue pregnancies, have an illness, feel abnormality there. There's a lot of complications involved here. There may be two new Carlos for you to address but there's a viewer that asked about today's Bradwood decision out of Texas. And how does that inform the discussion, could we see companies who do not want to ensure women who previously had abortions on religious grounds. Do you want to weigh in on that and do you know anything about it. I have not read that case because I also do corporate law and I do. Our reporters here for public are are keeping abreast of these developments and trying to make sure that the big themes that are coming out of this in this landscape that we're addressing those in our in our coverage. What about providers at one of our medical healthcare providers asked what about providers who have privileges in multiple states, meaning if I provide legal abortion care services in my state but also provide non abortion services and a neighboring state where abortion is illegal. This person could be at risk for losing their license I guess and then they bring state right. So there are a lot of I mean, I'll start by saying this I am providing no legal advice to people who are performing abortions on your expertise. Yeah, yeah. But there are, you know, there are a lot of questions that are going to have to be sorted out right so the most sensible answer would be if you're providing abortions in a state where it's legal to provide abortions and then you're also providing non abortion related abortions elsewhere, you should be fine. The problem of course is what Carlos was talking about earlier which is some of these statutes are do seek to sort of cross borders. And the question will be, you know, is there any way for a state to enforce their ban against a physician who shows up in their state because that person is providing abortions elsewhere. And one of the things anytime I get a chance to tell the joys of living in New Jersey, which is where I happen to live people can make their jokes if they want to. But you know New Jersey past of reproductive freedom act not too long ago, and then after Dobbs found New Jersey also, we've already sort of taken steps to protect specifically providers so and patients who might come here for abortion so if we get a subpoena where you're not going to send anybody's medical records, you know, those sorts of things. And I think that that's really, a really important thing that pro that pro pro abortion and pro choice states can do to protect health care providers and patients. Let's see, we have a viewer asking about the North Platte Nebraska case where the mother and daughter were punished based on the Facebook messages and securing abortion and just not necessarily just that case but what are the implications here for digital privacy. You have, you know the period trackers and things like that. Talk a little bit about that landscape. I mean, I've been letting me I've been reminding people that all electronic communication is trackable. And so just because you're not a text message if you're sending a Facebook DM a Twitter DM, a message on Instagram. I mean, I guess we consider signal to be secure like that's how I usually, or people who work in the administration, but you know that the problem electronics is it creates a trail. You know, and I know a lot of stuff went around about, hey, everyone wants to use our period trackers so that like they can't, you know, figure things out. But, you know, I think the only thing that's safe is old school communication. You know, if you're planning an abortion, maybe pick up the phone and don't send a text. If, you know, maybe don't use that period tracker, and maybe just use an old school calendar and go back to use to do because everything electronic is keeping a record and it just depends on whether the company is going to respond to subpoenas or not. By the way, we do have on on the public is website ways to contact us securely and we take that security very seriously for people who want to provide us information on any topic. Kim or Carlos or both of you, you know, Tennessee has a law that includes language about how the mental health of the pregnant person if they are threatening suicide does not count as a threat to the life of the pregnant person. Have you seen language like that elsewhere. I haven't seen language like that necessarily elsewhere but that is certainly the case at other states do not have health exceptions at all, and that the only exception is a life exception. And so that's leaving out all sorts of things right it's not just it's leaving out obviously psychological harm it's leaving out mental health issues it's leaving out for instance somebody who you know let let's imagine that you get diagnosed with cancer during your pregnancy and you could wait and then you could start cancer treatment after you're not pregnant anymore but that potentially reduces your ability to be cured right so you know there are a lot of different sets of circumstances short of death. So if the states are saying well then that that's just not good enough. And, and as much as I can criticize row and Casey and both of them are worthy of deep deep criticism. The one thing that the court kept coming back to was one you have a constitutional right to an abortion, and two, even in those cases when a state can ban abortion they have to have an exception for life, and they have to have an exception for health. And that simply doesn't isn't there anymore and mental health is health, you know, I mean that I think that that is forgotten. What about the enforcement of these laws, there was a I think 80 district attorneys mainly urban counties who penned a letter saying we're not going to enforce these prosecution is a decision that prosecutors make. And in the file every case it comes to them they decide what they want to what their priorities are.  I think so but I think that's why next frontier is the civil action. You know, I'm from Texas originally, and I know that in Harris County Dallas County Austin County, you know the liberal places, I don't see those DAs prosecuting abortion providers, but I do see people filing lawsuits against people who who are having abortions. You know that's the problem as well and then when it comes to abortion providers and hospitals, you know, it can be bankrupted by litigation even if it's wrongful. So the mere existence of these civil actions can act as a de facto ban, even if there isn't a total ban. I want to really follow up on that because I think it's such an important point here. The fact of the matter is is we're not seeing, you know, huge amounts of enforcement of these bands because they don't have to write that the that the that some of the power a significant part of the power is that people don't know what they can do, or people don't know what's going to be prosecuted. And in that set of circumstances, people are being enormously cautious. And so, you know, it's not even necessarily right there. We're not seeing any states doing huge sweeps, right, and catching people because they don't have to they just have to create enough fear that people won't provide the care anymore. And then on the point of, you know, district attorneys, there are a few things. So one is, nobody wants to count on their DA being one who's not going to prosecute, right? You're just sort of crossing your fingers and hoping that you're in the right in the right place. Two, we've already seen at least one governor say I will remove you from your post, because you have said that you're not going to be willing to prosecute these cases. And then three, lots of DA's, you know, they're elected. So they're not just they have to be thinking about what are the consequences if I'm if I'm saying I'm going to refuse to do these kinds of prosecutions. When I go back up for reelection again so there are a lot of things that folks have to think about here, in terms of whether whether and how the criminal justice system is going to be used against both pregnant people and people who provide abortions. Great, I'm going to pose two more questions and then we're going to wrap it up because we are getting to the end of our hour and it's flown by it's just been such a fascinating discussion. I wanted to ask you guys to, if you can summarize the most impactful legal strategies to date by states outlaw on outlawing abortion like, I don't want to say successful but what, you know, of the legal strategies to date, what are the restricting abortions, which have had sort of the greatest impact. I mean the greatest legal strategy is a ban. Right. The greatest legal strategy right now is a ban and then what we're going to start to see is what, what amount of ban is okay. So, you know, we're going to see people saying okay if a ban doesn't have a life exception then it's got to be, then it's got to fall if a band doesn't have a health exception then it's got to fall right so we're going to see this sort of process of trying to make sense of exactly can states go and you know one of the other things that I'll say is that what what we also got in Planned Parenthood versus Casey was that states could not require a husband's consent for a married woman to terminate a pregnancy. That's no longer the law of the land right so let's see what states do with that. And so I think that you know the most the, the, the most drastic thing that a state can do is say, you cannot do abortion, you cannot do abortions in any set of circumstances in this state, and then it's all going to be about sort of building back to figure out where, where are the real limits to what states can do. And I just add, you know, the second best strategy to an outright ban is this asking confusion, and we were experiencing it pre dogs, when, you know, there would be an abortion ban and get stayed and people were not sure whether they can get an abortion or not and so you know abortion clinics would not have anyone coming because people weren't even sure even when abortion was legal. And you kind of have seen that in states like where it's like it stayed now it's, oh wait it's back on it stayed now it's back on. That is as effective as an outright ban. People believe. Yeah. Right. Interesting. So I've got one more quick question and then we're going to wrap it up with some resources to leave our audience with. What do you all see for the future of contraception there've been many people concerned that we got a slippery slope that contraception is sort of the next thing that abortion opponents will turn to to try to restrict outlaw remove. Do you all see that happening. Yes. It's all I mean it's all a part of the plan. Right. I mean I think that's really important to keep in mind that that that the folks who are pushing hardest who were pushing hardest for overturning row. That's just a small sliver of an agenda. There's a lot of things and this opens the door to a lot of those other ways of controlling people's sexuality of controlling how people and with whom people procreate of controlling who people marry. And you know there's a lot of space that has been opened now and there's a I think there's a sense among lots of folks on the right that we've got momentum. Now is the time to really move forward with some of these things that might have seemed really extreme, even just a few months ago. And of course, outside of the issue of whether these folks think contraception is okay or moral issue. It can also be used in some cases to to after the fact, like plan B. So that's. So I want to leave our viewers with some good sources of accurate information that the public can turn to in order to understand the laws in their state, as well as how overturning row we wait is impacting their state you guys have any like what are your top picks top recommendations. I both recommend that my institute. It's like, it is the most accurate up to the 50 state surveys of information. And that's usually my first source that I go to. But I will also say, you know, most of the general press seems to be at right I think that the press is doing a good job of reporting on this. I'm, I'm not seeing much misinformation from like mainstream media sources so you know if you want statistics and data that I don't know, but just keep paying attention to the news on this. Right, it is it has been a very difficult thing I can say for many in the media to cover because it's playing out in this very piecemeal patchwork way. I wonder for example, have have women died if there've been any, any, so people have not received that, you know, immediate medical attention when needed. I think we really have a good way of getting our arms around the actual, the actual human harm here. Can I, can I add one thing to that though which I think is really important.  So, we're going to see women dying, and we're going to see women dying at a higher rate, because they will be forced to carry pregnancies to term in a country that does not care about keeping pregnant women and new mothers alive. And that's just the truth right so abortion ban aside. This country has not cared enough about women to keep them alive. And this is simply going to increase the number of women who died in childbirth or immediately after childbirth. I mean, we have an amazing 2017 maternal mortality project called Lost Mothers and Cameron, if you can, Connor if you can drop that link in the chat for people. It really explored that whole issue which is definitely related to this discussion today. Yeah, that was that Nina Martin and a lot of other folks from ProPublica put that together a lot a lot of work and really told the story of who's paying the price for that issue in America.


Soak your conduct's multilateral training with Moldova. Moldovan First Infantry Brigade, Special Forces, showcase their skills, in a culminating event during a multilateral training exercise, at the Bulboka Training Center in Moldova, November 1, 2023. Training between the Republic of Moldova, Romania, the United Kingdom of Great Britain and Northern Ireland, and the United States strengthens international stability, in a never-evolving security environment. U.S. Special Operations Command Europe conducts frequent buy-in multilateral training exercises to hone interoperability with allies, and partners to ensure readiness in the face of emerging threats.


The paper proposes a novel methodology for the analysis of variable angle tow, VAT, laminate structures using Reissner's mixed variational theorem, RMVT. This technique is applied to a Carrera unified formulation, CUF, finite element model to analyze the free vibration behavior of VAT plates. The proposed approach is compared to Abacus 3D reference solutions. Classical theories and literature results to investigate the effectiveness of the developed models. The results demonstrate that mixed theories provide the best approximation of the reference solution in all cases. This article was authored by Gaetano Junta, Domenico Andrea Ayanata, and Marco Montemuro.


Hi everyone, Joe for Jasper's case breaks.com coming at you with 2019 Panini contenders football hobby edition one box random team break number four with a big game mixer spot being given away It's gonna be a lot of fun. But first the break itself big. Thanks this group for selling out the box appreciate it all 32 teams are in Let's roll it. Let's randomize it two into three five times for names and teams different dice will for the giveaway part at the end of the rate one two three four and five Two and a three five times for the teams one two three four and five All right, so here is the first half of lists right there and The second half of the list right over here No trade windows. Let's alphabetize And print this out. Here's the print out hot off the presses Chew Tuesday the 7th. Thanks everyone for getting in. Good luck. Some of the guys were looking for right there well 2019 set like Daniel Jones will probably get Get that second contract with the Giants, I think he's proved himself Let's get some more weapons around them. I'll probably Probably be a good good idea They got a resign say quant to right think that'll probably be a good idea And then all the usual stuff teams need offensive line Maybe another past catcher The Giants they could use that Either defenses are they got that cave on tibet oh on the defense if that I think looks pretty solid Tyler Murray's this year too, but we're not going to see him for for a little bit All right. Good luck everybody. We'll kid reporter cards points that usually takes the place of An auto here's the auto Travis Fulham Rookie ticket autograph for Detroit. That's going to go to Brian Frank. So the points that'll be the Consolation prize will the name on top will get the Super Bowl mixer spot, and then the second name will get the get the 250 points Bruce Smith a legendary contender for sure going to Brad and Buffalo We've got playoff ticket autograph Eric Dungey 45 out of 99 Rookie auto for the Giants that's going to be for Tristan and a Cleveland feral cracked ice autograph 21 out of 23 for my Raiders chat with the Raiders Well, I mean They definitely reach for this guy in the draft, but They didn't get it. All right season last year It's got a great season and a redemption and the redemption is going to be Damian Harris Now it is expired. This is for the Patriots. This is going to go to Carl. It is expired, but you can probably reach out to them and probably get this card or Something commensurate to that Points wise So that's the break now who's going to win that Super Bowl spot? only one winner from this list But a chance to get a big game mixer spot for a fraction of the price Fingers crossed And good luck everybody when randomized this list four and a four eight the hard way one two three four five six seven and eighth and final time four and a four eighth the hard way Now again, this is tough stuff, but a lot of sad faces, but remember we've got a number of these fillers to go. So We have a number of these fillers to go. So if you don't get him this time, we'll get him next time. All right Oh Chad very close, but not quite you do get the 250 points consolation prize But appreciate you and everyone else trying name on top happy times for Carl There you go Carl. Congrats to you. You got into the Super Bowl mixer for a fraction of the price appreciate you getting in I'm Joe for jaspercasewrakes.com for the rest of you. We'll get him next time Oh, and you're part of that promo too. We're doing that randomizer right after this jaspercasewrakes.com


Welcome to model 34 of point set topology part 1. Last time we introduced the notion of connectedness, motivating it from the notion of path connectedness and then relating it to intermediate value theorem, least upper bound property etc. So, we will continue now the study of connectedness. So, here is a simple theorem which says that if you have a continuous function from one space to another space, it will take a path connected space as well as a path connected space whatever to the corresponding the image will be connected or path connected. So, it is actually two different statements here. By taking a subset Z which is say connected or path connected and restricting the function to that and to the domain FZ on the co-domain FZ, we can as well assume that F itself is surjective and make the hypothesis that X itself is connected or path connected. So, let us first look at when X is connected. I want to show that Y is connected. So, take a separation of Y, Y equal to a separately, it pulls back to a separation of X via F. So, all that you have to do is F inverse of A, F inverse of B that will be separation of X, pure synthetic thing. Continuity of F is used only to see that these two sets here F inverse of A and F inverse of B are closed, disjointness, union is the whole of X is all pure synthetic. So, that proves that image of a connected space is connected. Now, let us assume X is path connected and we want to show that Y is path connected. So, remember now I have assumed F is surjective. So, given any two points say here A and B, sorry X and Y or X1 and Y and whatever, they are F of A and F of B for some points A and B instead of X. But A and B inside X can be joined by a path omega or gamma. Gamma is a path in X joined A and B.  That shows that Y is path connected. So, we had defined long back that a property of topological spaces is said to be topological property or a topological invariant if the following holds. Whenever P is true for a space, it must be true for all spaces Y which are homeomorphic to X, which are homeomorphic to X. So, that was the definition 1.59. I am just recalling it. So, because image of a connected set is connected automatically under a homeomorphism image of a connected set will be connected because homeomorphisms are on to. So, homeomorphism preserves connectivity. Similarly, it preserves path connectivity. So, these two are topological invariants. Because of this property, what happens is whenever you are studying some connected spaces and so on, you can actually assume the whole space is connected, concentrate on a connected part of it and then discuss the whole thing. Because once you have that continuous functions from there will be always inside another connected set. After all, we are all the time studying continuous functions. So, lot of such discussions can be isolated just around a connected set. So, this leads us to the notion of what is called as connected components. Suppose Z is a connected subset of X and X has a separation, then either Z is inside A or it is inside B. So, this is the property of a connected set. Otherwise, what happens? You look at the, you know, you have to just take the restriction to Z, Z contained in ZX, Z intersection A, Z intersection B. That is separation of Z. Only thing is you do not know whether each of these subsets are non-empty. Z intersection A will be non-empty if Z is, you know, not contained inside B and vice versa. If not contained inside A, then this will be non-empty. So, if both of them happens, it should be non-empty and that will be contradiction that Z is connected. So, one of them must be empty which means Z is contained inside the other, either A or B. Okay. Therefore, what happens is, okay, let us, let us understand one more thing about this connectivity. Suppose you have X as a union of two subspaces which are both connected and the intersection is non-empty, then X itself is connected. Later on, we will generalize this one. Okay. So, this is just a trick using the previous lemma. Suppose this union has separation. Okay. I have assumed that X1 intersection X2 is non-empty. So, take X to be a point in the intersection. Then X being a single point, it must be either inside A or B. So, you can assume it is inside A by changing the notation if you want. But then, from above lemma, it follows that, you see, X1 contains little x, right? And that is connected. X1 is connected. Okay. So, Xi must be contained inside completely inside A. It is contained inside A or B is the previous lemma. But since already X is inside A, it is a common point with X, X1. So, it follows that X1 is inside A. The same argument for X2 also. So, both Xi's are inside A. That means B is empty. So, that is a contradiction. This just means that there is no separation of X. And hence, X is connected. So, you can see that already this is very easy to generalize this for any family X1, X2, Xn, not necessarily even finite. Okay. Here, I have not used any indexing set as just 2 here. This can be just arbitrary indexing set. It will be applying for all. That is just an observation you can make once you have understood for X1 and X2. So, now we make a definition motivated by especially this lemma. Okay. And then this corollary theorem here. Okay. Let P be a statement about subsets of a given set X. This is a general definition first of all just to tell you what is the meaning of this maximal. We say a subset of X is maximal with respect to P. First of all, it must satisfy P that property whatever. So, A satisfies P that is necessary. Then among us all those who satisfy you know this P say suppose B also another member which satisfies P. Okay.  So, if B also satisfies A must be equal to B. A is contained inside B and B is also satisfies this A must be equal to P. This just means that if I take slightly larger subset strictly larger subset then it will not satisfy P. Okay. So, this property P must be for subsets of a topological space X that is the whole idea because it is a topological proper 10-way road. So, whereas this definition is for all this is just a synthetic definition. There is no topology here. Now we are going to make it a topological property especially take P to be property of being connected. In other words look at all subsets of X collect all of them which are connected into a subspace. So, that will satisfy P. Right. So, P is a subset of the power set of X. All elements are connected to begin with. Now you take a maximal element inside this collection. Okay. That means anything every element here is connected first of all and anything slightly bigger than A will not be connected. Okay. That is the meaning of maximal element. Okay. So, we can make that as our definition now. Let us see. Let X be a topological space. Then every point X belong to X is contained in a maximal connected subset. Thus X is the disjoint union of its maximal connected subsets. If I prove the first part then the second part is purely set theory because every point is in a maximal set. The union of maximal subsets will be the whole of space. So, we want to prove that each point is contained in a maximal connected subset. To begin with singleton sets are connected. Right. So, they are the members of this set of all connected subsets of X. All right. I want to show that it is in a maximal set. Everything every X must be in a maximal set. That is what I want to show. Okay. So, now use this property to become, you know, to make, to grow this set point, single point into a maximal set. That is what we want to show. This property we keep using again and again. So, here is the way how to do that. Define a relation. I am saying here is a way. There is not just, this is the only way. There are many ways. For example, you can use John's lemma and so on. I do not want to, I want to do it very elementary way. Define a relation R on X as follows. X is related to Y if and only if there exists a connected subset T inside X to which both X and Y belong. Both X and Y belong to T. Singleton sets are reflexive. So, I do not have to take anything. I can take T as singleton X. Then X is related to X. If X is related to Y, XY's are both inside T. So, Y is also related to X. Transitivity is previous, is precisely what is needed and that is previous theorem. If T1 is containing X and Y and T2 is containing Y and Z, then what happens? T1 union T2 will be connected because they both of them have common point Y. T1 and T2 are connected. They have common point. So, union is connected is a previous theorem. So, I have found a connected set which contains X and Z. So, transitivity follows from the previous theorem. Therefore, this R is an equivalence relation. As soon as you have equivalence relation, you have a partition. Then this is the second part was precisely a partition. What is partition here? X is the disjoint union of maximal connected subsets. So, each member of the partition is a maximal connected subset. So, that is the part directly improving here. That will give you that every point is inside a maximal connected subset. So, these equivalence classes are I have to show connected and they cannot be bigger. If you put any more point, it will be disconnected. That is a maximality. To show that it is connected, take an equivalence class. Suppose there is a partition, pick up an element A in A and B in B. But they are in the same class which means A is related to B and hence there is a common connected such T which contain both A and B. But T be connected, it should be either in A or in B. That is a contradiction because one point is inside A, another point is inside B. So, T is first of all a connected subset and C is the equivalence class of all of them. So, T, all the points of T are inside C first of all because T is connected. All elements of T are in one single class and A and B are in C. Therefore, the whole T is inside C. So, but this partition for T intersection A, T intersection B will be a partition or T that is not possible. So, the different ways of arguing, I can just show that T, previous term already T has to be contained inside A and B. So, that is not possible. Therefore, C is connected and there is no partition like that, there is no separation like this. Therefore, each equivalence class is connected. The equivalence classes are already partitioned. So, anything bigger than that cannot be connected. But if it is bigger than that then it is not a class, it is a bigger class. So, these are actually maximal connected sets. So, it is better to give a name for these maximal connected sets after all. All the time otherwise you will have to keep on saying maximal connected, maximal connected. So, such things are called connected components and quite often when you are discussing connectivity, you will just say component. That is the whole idea of naming this. I mean this definition is just for the name sake. Precisely, I mean literally it is for name sake. Let Z contained inside X be a connected subset. Then the closure is connected. Now, why we are having such a thing? You see, now we want to understand what happens to connected components. They are already giving you partition of the whole space. Now, this theorem says that take a connected component. Closure is automatically larger, but it cannot be larger. It has to be equal because closure is also connected component, connected subset. Being Z being connected component, anything bigger cannot be connected. Therefore, there must be equality. So, this theorem tells you immediately that connected components are closed inside the original space X. So, let us prove that Z bar is connected. Assume Z bar as a partition, A, B, separation. But then Z is connected.  This was our old result about closures. Therefore, Z bar is either inside A or inside B. So, there is no such separation. So, you see several of these results we have been reducing by contradiction. Why? Because the definition of connectivity itself is in that form. That is what I meant by it is some kind of a negative definition. Path connected components are also defined the same fashion. What is it? Maximum path connected subsets of a given topological space. So, you can also say that just the equivalence relation is that if X is related to Y, there is a path from X to Y. No need to have their path connected component. A path, image of a path is already a path connected space. So, this is slightly easier to digest equivalence relation. In fact, usually whatever happens to path connected spaces, you try to copy it in connected and if it works, it works. So, that is the way that perhaps this theorem has been used here. This definition has been done here. So, path connected components also give you partition of the whole space. One has to be very careful when you keep saying it is same thing, same thing, same thing. It is lot of close relations but they are after all different notions. So, somewhere they will be different. So, that is what you have to be careful about. That X be a topological space and X belong to X be any point. Then the set of all points of X which can be joined to X in X is the unique path connected subset of X containing that point. So, this is another description of path connected components. Start at any point in a space, look at all those points which can be joined to that. So, that has to be obviously that is path connected that has to be the component. If there is another point that can be also joined, it is already there. That is all, very easy to look at this way. So, that is no need to write down formally the proofs of this one. This is where I want to caution you that path connected component need not be closed. In other words, if Z is path connected, Z bar may not be closed. If that was the case, then components would have been closed. So, we will see an example little later. Secondly, if we have homeomorphism from X to Y, then look at the path connected components of X. They will go in one-one fashion to path connected components of Y. Exactly, the components of X, connected components of X, they will go in one-one fashion to connected components of Y. In general, path connected components are connected also that we have seen. But number of connected components may be larger than the number of path connected components. But this correspondence is true for both of them.  You can do that by component wise, restrict F to one component here. When you go to the image, it will be another component there. Therefore, right in the beginning, you can assume that both X and Y are connected by restricting the whole thing to a connected component. So, this is how I already told this one, but I have repeated it now. So, next time, we will make sure that you will be able to see a counter example also for this. In any case, we have a lot of work to do about connectivity. Simultaneously, whenever such things are true for path connectivity, we will keep informing you or we will keep pointing out to you. Let us stop. So, until next time, let us stop here.