Continuing with the study of CW complexes, now we take up the topic of homotropical aspects. One of the easy consequences of so much of study of the product that we did, once you have a CW complex X, X cross I will be automatically a CW complex now because I itself is a CW complex which is compact. Therefore, construction on functions, continuous functions on X cross I which is same thing as homotopy becomes easy. So, this is the first theorem that we have here take XB as CW complex. A function X cross I to Y is continuous if and only if restricted to each X k cross I, all these restrictions are continuous for each k greater than or equal to 0. What is this X k? X k is kth's character. So, all that I have to say that the coinduced topology with respect to this family X k cross I on, so in the entire X cross I, the same thing as the ordinary product topology which we know is equal to the coinduced topology on X cross I. The coinduced topology on X cross I is the general thing namely by compactly generated sets. Or you can take coinduced topology on X which is through this family 96 and then take the usual topology on I and then take the product and see what it is happening. So, whichever either two ways you have to do. So, what I do? Look at the identity map from X cross I, the coinduced topology namely X cross IW to X cross I. This is homomorphism because X's compactly generated topology and I is compact. Therefore, function f is continuous on X cross I if and only if a restricted to X cross I, the kth skeleton of this is continuous for each I because I have to verify it from this topology. The kth skeleton of X cross I is remember it is union of various we can take X i skeleton and then Jth skeleton, but I has only two skeletons 0 and 1. So, it is X k cross 0 union X k minus 1 cross I. Those are the two skeletons. In any case for each k what happens is the kth skeleton of this one is obviously contained in X k cross I which is the full k plus 1 complex and that is contained inside the k plus 1 skeleton of X cross I comma W. So, these cross subsets are trapped between these two things. Therefore, whether the coinduced topology is with respect to this family or with respect to this family they are the same. So, once you have this readymade criteria what you do is you construct homotopes on the 0 skeleton extended on the 1 skeleton extended on the 2 skeleton and so on as homotopes then you put them together automatically it will be a continuous function from on X cross I. So, this is the idea of this theorem. This is how it will be this theorem will be used now. Now, this is the central result for all homotopy aspects of a CW complex. So, which we have prepared long back right in the beginning in proposition 2.1 that U be an open subset or a closed subset where X A is a relative CW complex.     The easy part here is each U n minus 1 is a retract of U n then we know composites you can take composites or retractions retractions two retractions you take composite to composite to retraction. So, you can take finitely many composites each U n will retract to U minus 1 that is easy after that U will be retract because I can define the retraction on U to be these composites depending upon where my n is where my x is every x is inside some R n sorry inside some U n right because every x is in some way x a n skeleton. It may be starting U minus 1 itself there is nothing to do there you define it as the n composition. So, that is the easier part the thing is how to get homotopy you cannot compose homotopes so easily because they are not dominant code of means are different. So, let us go through it carefully that f n from U n cross i to U n be a homotopy of the identity map and which is relative to U n minus 1 because all the points of U n are fixed okay f n of x 0 is x is identity map is to begin with and then what you have is the nth function f n of x which is f n of x comma 1 this is by definition okay that is a deformation retraction that is a retraction whatever U n to U n minus 1 automatically once you have such a thing okay.  So, this is a this is the hypothesis that is given that each U n minus 1 is a strong deformation retraction of U n okay. So, the last map which is a retraction I am taking f n okay this is a strong deformation retraction for each n that is that is the meaning given by f n itself there is nothing more than that therefore if I take composites g n is f 0 f 1 f n we get a strong deformation retraction g n from U n to U minus 1 okay. I do not know that but I can definitely say that this is a retraction this is a retraction okay. So, we do not know whether it is strong deformation retraction but we will see that soon okay.  So, it will be just the rest of this f n plus 1 you compose it first f n plus 1 of some x if it is an element of U n it will be just x itself and then rest of them is g n. So, this is the important thing here therefore if I define g as g n x whenever x is in U n this will be well defined function on the whole of U. This map will be actually from U to U minus 1 okay and this is retraction because points of U minus 1 all of them keep fixed okay.  So, that step is a lesson here in getting how to get compositions of deformation retraction or homotopes in general what composition infinite compositions okay so you have to watch it carefully okay that itself maybe the step itself will be useful elsewhere also. So, look at here what I do I start with f naught okay and this first half of the interval I will keep it idle identity then I take f naught. So, this is my g naught times trying to define a successive way of composing okay so in the next step I compose I define g 1.  So, next step I will cut down this one again identity up to one fourth itself then whatever f 2 you have got you plug in that one here and then the entire earlier stage g 1 this entire the re-parameterize from one third to one so put that one here. So, this is the way I so at the end the stage 0 to 1 by n it will be identity 1 by n to the next 1 by n plus 1 it will be f n minus 1 or f n whatever and then the earlier homotopy which you have constructed this is the way I am going to do okay this is just a schematic way but now I will have to write down exactly so define g n inductively okay g n from u n cross i to u n inductively as follows g naught of x t see this step was given due to g n so inductively defined how g naught of x t is x in the half first half of the interval then it is f naught of x 2 t minus 1 half less than t less than or that you have to say that when t equal to half there are two definitions they must coincide okay when t equal to half what is this this f naught of x 0 so it is identity it is identity here. So, for n greater than or equal to 1 having defined g n minus 1 you define g n as x in the interval 0 to 1 by n plus 2 if n is 1 this is one-third okay like this here second stage is one-third okay from 1 by 1 divided by n plus 2 to 1 divided by n plus 1 you put f n of x appropriately you know scaled you have to appropriately scale this the thing is the thing that you have to write correctly okay for example when t equal to 1 divided by n plus 2 what it this will be n plus 2 n plus cancels out so this 1 minus 1 it is 0 okay this f n of x 0 okay when t equal to 1 by n plus 1 this will be n plus 2 divided by n plus 1 which is 1 divided by n plus 1 minus 1 n plus 1 cancels away so this will be what this will be equal to 1 divided by n plus 2 I am sorry not 1 divided by f n of x 1 it will be so like that you have to see the that they match up okay so here you take g n minus 1 of not g n minus 1 itself but put f n of x t so this is the difference I which was not explained here what g 1 I have but this is just a diagram okay so that at n equal to at t equal to 1 divided by 1 plus n this will coincide with f n of f n of x t little f n of x 1 it will coincide okay so definition of g n is clear how to and one does it now having inductively we have now we know verify that each g n is a strong deformation retard of u n into u minus 1 so this was the claim there okay but there we knew only retraction now it is proved that each u n retracts to u minus 1 in a strong deformation way moreover g n restricted u n minus 1 cross i is g n minus 1 whenever it is inside u n minus 1 it is it is g n minus 1 therefore there is a well defined map g from u cross i to u given by g of x t could g n of x t whenever x is inside it if v is an open subset of u I have to show that why this is this is continuous but this is more or less obvious from the co-induced topology peak topology what is the inverse image g inverse of v g inverse of v intersection with nth skeleton the same thing as g inverse of v intersect with u n but that is g inverse of v intersection u n is what x a n skeleton okay and at g n level it is it is a continuous function so this is an open subset of x a n for each n so this means g inverse of v is open inside here okay therefore g is a continuous function so that g is a strong deformation retract of u into u minus 1 is directly verified because once from something is in u u minus 1 all the time no matter what the second coordinate are there these functions will fix the point no matter what they are all of them are identity g n of x this f n of x is also x g n of that one is also x and so okay so that's why it is a strong deformation attraction of of u onto u minus 1 now we can have nice theorems like this which we want to remember forever you may not be able to remember immediately how this is constructed you may just whereas you should remember this way the picture here then these formulas nobody remembers them you have to work it out by yourself so that things match up correctly what you want two functions are two continuous functions when they define continuous function on the intersection of these two on the neighborhood on the set of points where in that and they must agree that's all that kind of things is what you have to do okay so what is the theorem theorem is that every c w complex is locally contractable right in the beginning we told you that these c w complexes must be having lots of euclidean property every euclidean space every open subset is locally contractable okay inside r n so that properties here also later on when we define manifolds you will see that manifolds are locally contractable because they are locally actually euclidean spaces so c w complexes are that property it's a very important property so how do we improve this one what is the meaning of locally contractable first of all even a point x and an open subset we contained in containing a point we have to have a subset of that which is open and a containing x and that must be contractable there is slightly weaker versions also but we are not satisfied with weaker version we are going to prove this stronger version so every open set contains an open set okay contains a neighborhood of that point which is contractable that that point that neighborhood is contractable this is what we have to prove all right so using the previous lemma this this this homotopy lemma whatever okay what we want to do is we want to construct it inductively okay skeleton wise so this construction is done inductively to begin away there is a unique open cell ek in x to which x belongs to so this is again and again used what is that namely a c w complex is disjoint union of its open cells so take the open cell to which the given point x belongs to okay first choose a contractable neighborhood uk of x in ek because ek is a it is some defumorphic to some homeomorphic to some is a dk right there you can find intersect it to be that will be an open set inside dk x belongs to that open set inside that you can actually choose a neighborhood which is like a bar homeomorphic to a say an epsilon bar that will be locally contracted to first choose a contractable neighborhood uk let us call it uk of x inside ek so that even the closure uk bar is contained inside p intersection ek bar you can take as small as you want closure should be there the closed wall it should be there that it and now for n greater than equal to k having constructed a neighborhood un so that the closure of un bar is contained inside xn intersection v okay so you can make this one the yi to closure so that this closure is compact and such that un minus one the other thing is a strong different tract of un okay so this is an inductive step the inductive step is carried out as follows so you have to how to how to take the un right once i do that i am done because then i put union of u and the whole thing will be over so how to construct this un so let lambda be the indexing set of all n plus one cells from xn you see i started with xn itself here or because sorry ek ek itself k great now n up to n i have un minus one i have done now i want to un i have done sorry un i have done this one un plus one i want to do is in this inductive step is like that okay u minus one here is actually equal to the disk this disk itself that uk bar that we have taken below that there is nothing because x itself is in the kth skeleton right it is in the open part of the of a kth skeleton of a cell there okay so from n to n plus one i would like to do this step now to look at all the n plus one cell index them by lambda for each alpha in lambda we have phi alpha inverse of un bar which you have constructed un bar is compact set phi alpha inverse of un bar is a closed subset of sn so it is a compact subset of sn okay contained in the open set phi alpha inverse of v so your compact subset contained inside a closed subset of a compact so compact inside v so therefore you can find an epsilon which depends upon alpha okay between 0 and 1 such that if you construct remember this step before the lemma before 2.1 this n epsilon phi alpha inverse of u alpha that is some a its closure is contained if we alpha inverse of v so all the epsilon viscose will be contained in that is one will be taken so this c is an open subset its closure is contained again okay with this way for each epsilon for each alpha I have chosen an epsilon so I have function here okay then you define un plus one to be n epsilon of un which is union of all these things along with un that is the definition as defined in 0.1 now we take u equal to un from lemma 2.1 follows that it is a contractable neighborhood of this one okay so basically it is the lemma 2.1 which is employed here okay and prior to this proposition 2.1 it actually proposes 2.1 the next theorem is about the cofibrations and so on so let me just begin this one with a lemma and then we will stop and take a break okay so x be obtained by y by attaching k cells okay see it seems that all our lemma start with this one the inductive step for CW complexes so that we can carry on with inductive steps inductive constructions so x is obtained from y by attaching k cells then look at x cross 0 union y cross i is a strong deformation retract of x cross i so this is a proof so let me go through this one and then stop again let us have this family of alpha alpha and lambda with attaching maps for the k cells one of the standard that we have proved in part one is that there is a strong deformation retract dk cross i where dk is a cell I mean dk is just the unit disc cross i dk cross 0 the bottom and only the boundary cross i so it is like a tub it is like a cylinder one top top open and bottom close cylinder that cylinder is is a strong deformation retraction of stronger to retract of the full dk cross i the the full cylinder okay so this is what we have this was one of the central results in part one let h from union the disjoint union of dk alpha cross i to disjoint union of these things is in the union of all such h that means I am taking the copies of h on each alpha it's just the disjoint union of copies of this h okay let f from disjoint union of sk minus 1 alpha cross i to y cross i be defined by using the attaching maps on the first coordinate is f alpha of x the second coordinate undisturbed t okay so these are the attaching maps for all all k cells once you have this what is the what is the space x x is the quotient of y x cross i is a quotient of y cross i disjoint union dk of alpha cross i right because x is the quotient of y disjoint union dk of alpha so x cross i is a quotient of this one this is this needs a a proof by the way in general this is not true that if x to y is a quotient map then x cross z to y cross z is a quotient map okay so you must have some hypothesis on z namely locally compactness and so on so this i is a compact sense this this is okay here this is general this is a fact by the one single identification namely this f is just composed of all f alpha right so f alpha is just x comma t t factories undisturbed x is identified as fx so this will give you the identification on the product x cross i as this as a quotient of this one that is just q cross i in any case okay so therefore what i have is y cross i disjoint union dk cross i all the cells to q cross identity x cross i i want to define a map here okay i have a map here already on the on the top on the product and disjoint union of these things okay on each on each part here it is a it is a strong distribution retract on the part why it is just identity map okay this on the part why it is just the identity map all right so what you do you have to just verify that this factors down to through identity quotient map that's all why because on the boundary wherein f alphas are being identified it is identity map the entire homotopy is identity map there that is why it works so you have got a map here to verify that this is a strong literature you have to verify it here so let us stop here and continue next time and we will come back to this important result how we are going to use this one thank you


o rookie to 499 i'll do it for your break there peter thank you again for the support man do appreciate it here and in group breaks we'll get them right out to you buddy another 20 for jeff now i got you i'll do it like i always when i did it last year i just did it during the break to just make sure okay um this is jeff m part of 20 look here jeff what's going on everyone whoa sam here with late sports cards we are gripping 20 2023 apne national vip silver packs for jeff m so let me count these up again for you jeff we got one two three four five six seven eight nine 10 11 12 13 14 15 16 17 18 19 20 yep look jeff drops kelsey quinton johnson to 499 from charges donovan michael and justin fields both base there okay interesting uh to russell wilson anthony richardson 199 for the colts nice jimmy garoppolo and deuce vaughn to 99 for the cowboys so weird seeing jimmy g is a raider both of them seem right jaylen brown and jimmy r gives the 499 for the lions kawaii and jordan love to 199 for the packers timely that they put him in this set very timely christian mccaffery and alan iverson 599 for the sixers where they had him as a nugget last year this is our rizley something weird carly three towns there's a blue dale earnhardt jr for a 50 out and do jordan love and brace sensabaugh to 99 for ohio state they're drafty this past year a kyle bush and brock lesnar 30 of 50 on the blue kody roads and hendon hooker to 499 going to the lions lines are gonna be a really good team breaks this year with hooker and kids they're gonna be so nasty jamar chase and jackson smith and jigba it's a 499 for the seahawks seahawks also with him and sherbin it was from uh damien let ucla i think kairi erving to 199 for the map i think it's ucla i don't know i'll drop my head dwelling bead and is our tomson to 599 to uh and purple 9 of 25 jonathan taylor the colt jo burrow and brace sensabaugh to 599 for ohio state the ohio state micah parson's orange tomorrow chase color match to 199 for the bangles oh we got an auto tray mcbride nice that is from 22 the rookie premiere very cool on-card tray mcbride now the cardinal of course there you go congrats on that jeff that's pretty cool and josh alan base first auto we've seen tonight at least out of these so far just one back to back jordan love wow holy cow 20 of 25 congrats jeff there you go buddy hell yeah dude and kevin harvick james hearted and case on wallace to 199 on the orange i'm doing for your uh packs there jeff thanks again for the sport buddy we'll get them right out to you my man got another uh 20 james uh yes i do sorry there you go james p coming up here good luck here james what's going on everyone sam here with late in sports cards we are ripping 20 silver packs for james p it's good luck here james let's see it uh let me count them out for you really quick james one two three four five six seven eight nine ten 11 12 13 14 15 16 17 18 19 and 20 that is awesome eklah da marino to 599 hit alton's that is a brock lesnar to 99 and kairi urban base red brock lesnar darry kenry and red carl anthony towns to 99 that is a rhea rippley to 199 and rhea rippley base kevin orange hendon hooker to 199 lions etch my homes and sax sharpenets to 499 for the seahawks on the rookie nice that is a bjohn robinson five of 10 on the gold gold rookie congrats james that's freaking awesome dude so cool bjohn for the falcons dany dimes there's a lamar and dylan michael to 599 university of texas orange bo jackson to 199 for the royals and anthony davis nice garret wilson on card auto oh heck yeah dude oh that's awesome i love these dude the the silver pack autos are always so sick congrats there you go james nice garret wilson rated rookie auto coming your way and darryck car got darryck cars a saint forgot about that too now that one's probably fine uh kiante george to 599 uh one card is jalen herz sick devin booker and erin rogers as a jet to 99 so weird dude orange jordan love to 199 and lamella rock lezner orange to 199 bjohn robinson jason herbert to 50 23 of 50 that's on that one there micah parson's base jason tatum and red to 99 anthony davis orange case on wallace to 199 199 of 199 on the orange smart chase roman reigns orange josh allen 199 devin booker and price young to 499 for the panthers nice one there that'll do it for your break there james pretty solid overall nice bjohn nice uh garret wilson auto we'll get him right out to you my friend john t coming up now all right good luck here uh john what's going on everyone sam here with late sports cards ripping one box of 2019 panini contenders oh that's 21 whoops my bad restart that let me go grab a 21 contenders one sec guys my bad the rb box jersey that's disgusting uno de uno sam casel good lord man with two one of ones wow what a box what a box man back to back one of ones skew henderson let's go skew henderson why are you gonna show that to us man one of one framed auto chef bagwell astro congrats straws one of one hall of fame framed autograph uh that's going to be our first one-on-one platinum foil kawaii Leonard that is nasty dude on the throwbacks raptors and clippers luckily this is a left side serial numbers break there's demons fettle and how about a red wave to five jokwon you rookie no way already boom there we go pitman had the gold of this exact card for you east that is some last pack magic right there steve let's go congrats matt jim brown out of four all pro just passed away in the past few days rest in peace jim brown for cleveland all right good luck here um zah john what's going on everyone sam here with late sports cards ripping yeah one box of 2021 panini contenders football hobby for john t so good luck john uh regular vet base will not ship out of john all your inserts hits parallels numbered stuff all will ship just no at least it's good luck buddy i caught that i don't see a t-law power players is there's Leonard the rookie of the year contenders jamar chase thanks timmy chain movers is mike ever appreciate that way jerry rice uh pete werner nice one there on the base rookie ticket auto for the saints peter verner combrey mvp contenders base auto jerry paterson for the commanders say bob greece i believe say andrew luck uh no dice roll trey lance and jack will that is a carlos a boogie bash um base ticket auto for the uh those gladiators of robinson and a that's awesome there's uh rookie the air contenders kyle straw dania is awesome erin rogers is a nice jaylon waddle rookie ticket auto for the dolphins congrats on that there john nice one there buddy base jaylon waddle take that for sure let's say daniel jones uh clio mac power players to 99 and jrombus say josh allen and tyson williams base uh variation rookie ticket auto for the ravens patch my homes that'll do it for your break there uh john thanks again for your support buddy get them right out to you my friend nice a little jaylon waddle action there john t your silver's right yes the next one we'll have to go and grab some more um i got rob w coming up next with some silvers good let me tag you off really quick rub oh come on really there we go tag you off rob ripped sam good luck here up what's going on everyone sam here with late in sports cards ripping 20 uh 2023 panini national vip silver packs for rob w really quick rob we'll go through them one two three four five six seven eight nine ten 11 12 13 14 15 16 17 18 19 and 20 so good luck here rob let's do it buddy kairi herbing orange to 199 it's 199 of 199 got some fields purple three white ed 25 that's on that for duke and nickley yolkich yolkich orange kovie buffkin to 199 or michigan shea gilgis alexander say kovie buffkin it's 599 for michigan red jamar chase 299 for the bangles and shrey young orange lebron to 199 kid conningham chase elliott's and jaden ivy to 499 on the rookie those sweet throwback jerseys say just a joe burrow bass in there they do yeah to 199 bijon robinson james hardin cal ripkin 599 for the orals their car 599 bow jackson say blue coat the american nightmare cody rhodes to 50 or wrestling action there's stuff curry that's ant man 199 t wolf joe erin rogers as a jet and jordan adison to 499 first adison we've seen for the vikings stef and the kid ken griffy jr 599 the mayors nice red anthony richardson 10 of 99 congrats on that one there uh rob jaw orange trey young to 199 erin rogers as a jet orange beyond cabell air to 199 and a luka it's a derek henry and shat holmgren rookie to 499 lastly oh we got a flood victor wendman yama wow that's so sick congrats on that one there rob what a last pack oh that's hot dude and he's in his uh he's in his spurs uni too that's great hell yeah man victor wendman yama wow and kd i'll do it for your break there rob congrats man couple of really nice carts got them right out to you buddy yeah yeah that'd be fun i grab a couple more boxes for tom here give me one set guys i'm gonna grab the rest of the personals you see with two one-of-ones wow what a box what a box man back-to-back one-of-ones skew henderson let's go skew henderson oh why are you gonna show that to us man one-of-one jeff bagwell astro congrats throws one-of-one holofame framed autograph uh that's gonna be our first one-of-one platinum foil kawaii Leonard the claw that is nasty dude on the throwbacks raptors and clippers luckily this is a left side serial numbers break there's the demons fettle and how about a red wave to five joke one you rookie boom there we go pitman had the gold of this exact card for you that is some last pack magic right there steve let's go congrats matt and browns jim brown out of four all pro just passed away in the past few days rest in peace jim brown for cleveland here one-of-one larry fits gerald star swan signatures wide receiver madness larry fits gerald he signed the whole lot recently that's a legend right there one-of-one logo patch auto star swatch that is from 2020 it is from 2020 actually larry fits gerald oh check this one out we got zool auto number to 50 it's gonna be bonix and kaleb williams boom sick one there kaleb williams the heisman trophy winner with the c as well on the patch 30 of 50 got the oakland days super rookie super won yippies rookie super fracter cardinals all right let me grab uh write down tom's name uh he's got good luck here calm let's do it what's going on everyone sam here with latent sports cards doing a pretty big mixer for um tom see we've got two 23 finest two superlatives 30 father's day packs 30 vip national breaker packs uh we also have two three and twos and one select a basketball um so we'll start with your father's day you've got three of or 30 of them tom we got one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen eighteen nineteen twenty twenty one twenty two twenty three twenty four twenty five twenty six twenty seven twenty eight twenty nine and thirty we'll start with the father's day uh pretty rare i have to imagine to be honest veto uh nemhard rookie micah parson's nemhard rookie again keegan murray two 199 rookie for the kings kory rhodes tanner mckay a palo rookie uh masatake yoshida and trevor warrens bunch of stuff in there three cards in that one that's devin booker and charlotte flair to 50 on the blue uh jordan lawlor nice one there to 199 as well as the dylan mitchell Perez and mac mclong rookie cool one there jaylon durin joe burrow one city towns and james wood it's kelsey anthony richardson rookie adan o'connell zane smith josh downs yana santa cumpo but keonte george drew jones the all-american nightmare cody rhodes pateese jordan lawlor ack mclong john morant sary eason gary goulding zion and travis kelsey to 99 jaylon herzen jay caner and the edwards marcella mire but shade on sharp korn adison and jaylon durin to 199 rookie for the pistons mleek cunningham nick bosa jade and ivy rookie kevindor ant masatake yoshida and aj brown uh josh allen blue jackson churrio to 50 the brew crew j jettos and palo rookie still at duke luka jackson churrio cj stroud donovan mitchell ellie and roman reins staff curry to 100 that is like completely bent i'll send the pack with you as well um one of the father's day packs that's destroyed i apologize on that tom uh we've also got 30 uh breaker packs one two three four five six seven eight nine ten one two three four five six seven eight nine ten one two three four five six seven eight nine ten oh that's cool jaylon brunson 199 and devin booker to 199 those are sweet dude oh we got an auto already it's gonna be an ebb and mobley nice one there knock numbered for the cavaliers that's gonna be honest to 199 jamar chase to 199 lamello to 199 aweson that glare to 199 there's a devin booker to 199 to the suns stef curry to 199 and gold flood jabari smith jr four of ten rookie for the rockets that's so sick congrats on that tom very nice one there buddy gold flood jabari smith i'd probably do that should be butler to 199 kd to 199 i think everything is in this is the number and that's good there's quail enter to 199 deandre swift as an eagle to 199 jesson herbert to 199 lamar jackson to 199 jo burrow and daniel jones both to 199 mahomes to 199 there's nikoli yokic to 199 lamello to 199 and eckler again to 199 okay just assume unless i say so it's just going to be numbered to 199 so that's going to be again numbered of jimmy butler and of kevin durant kawaii lenard and deandre swift again jesson herbert again and lamar again so follow their rolling thunder burrow and daniel jones both numbered homes and yokic parson's and travis kelsey you know our auto out of one of these 30 that'd be sweet a jaylon brown and jama rint donovan mitchell and cat jordan love derek henry juel ambide and two attack of iloa uh jesson fields cooper cup yes yes it was like yes in fact it was russ and jimmy garoppolo to 199 i think he might be trolling you i think he might be as well i might have to ban that guy james hoten and jonathan taylor jalen herz and kade cunningham uh to 199 to 199 lebron and jay jetis josh allen and damian lillard cup and jason tatum kd as a son and jesson fields dame dolla jimmy butler jama rint and josh allen i'm i'm getting rid of this guy all right tom will do two three and twos now 2023 panini three and two missy two man hope you're doing well up there dude we miss you a lot one of one zag veen all prospect team there you go tom congrats buddy good table yeah that was quick one of one platinum foil zack veen mean green veen as he's known as uh by me there's two 150 one marishall and frank thomas 20 of 20 got jersey card elijah green 14 of 35 player worn elijah green for the gnats and nice one here four of 25 shawn green that's pretty cool new players today played in the bigs from japan that's actually pretty sick four of 25 who is it your second three and two now tom is it it's it's it's not sasugo is it yoshi satsugo i think he played on the plate on the raise for a bit if that's the same guy we're thinking of nice that is a one of 10 buck lennard no it's just gonna save me a dom demaggio to 90 90 he was actually pretty solid for a bit i have his rookie i'm pretty sure i was like it's pink rookie or something from tops chrome and joe demaggio to 150 for the yanks got a patch card a brady house two of three prospect jerseys it's not uh affiliated but still nice and jersey auto daniel espino 88 of 99 all right tom we got your two finest coming up next two finest where are you at now blake uh stat island where's that uh uh new york oh okay crazy up there just because of how crowded new york right very true d l hall refractor rookie joey meneses refractor rookie auto nice one there corbin carroll and francisco alvarez holly to 125 green mini diamonds zack wheeler and logan web foglia headliners brice harper shay mclannahan boba shut stat island is a place that's for sure it's all marty refractor who's an army in ken walde chuck the j rod world's finest z field tovar masatake yoshida vladimir guerrero hose al-tube to 199 j ram and raffi devours blue bob hunter brown refractor rookie on soda al-tube headliners millen ryan blue jeter downs to 150 for the nationals and paul bulgeman the lever toward josh young and joey meneses and spencer steer refractor rookie yelich and freddy freeman seager cavalli j ram to 300 300 of 300 rally green and oscar jazala's headliners adrian belchai austin rye second box now a finest tom good luck here buddy that's o'neill cruise refractor according to lemons refractor rookie auto oh shut we got a gold uh one sodo headliners eight of 50 satara fujinami ken walde chuck sataka yoshida rookie dav winfield wit and tovar refractor j ram and base college trout judge rly rochman or tease uh on the um rivalries purple vulpita 250 rookie chotto and before though where bryce terrain refractor rookie joey meneses christian yelich say headliners tatsis refractor freeman and riley green say green josh smith j smoof to 99 i swung there for the rangers kenzala's hunter green say refractor rookie of brett baby austin riley corbin carol rookie migel cabrera 150 francisco alvarez and zack wheeler green to 250 headliners rafi devbers logan web and chain the plan ahead all right we've got a select basketball for you now tom 22 23 select the basketball and we'll end with superlatives westley 249 shagel just alexander throwback threads that's gonna be game used for the flippers this one there la jayland urin try color and drew holiday shade on sharp rookie i have to soon christian wood to 299 lake westley a j griffin jake larabia 28 of 99 rookie jersey auto on the purple for the grizzlies it's an anphony simon silver and kwai Leonard jason tatum unstoppable silver silver markinon and stuff and flago shagel just alexander and fred van leet filler jamal murray to 65 on the orange die cut jaylon williams malcolm brogdon scope and jalen green joellen bead to 175 and joellen bead you got it oh yeah that's a shade on sharp and james harden jeremy sohan keegan murray bronze to 49 nice one there congrats on that one tom keegan yannis jaylon durin zack levine there's benedict matherin rookie jersey card for the uh pazers nice one there silver kd and jeremy sohan hallow rookie jaylon brunson silver demar de rosen and damien lillard right we've got two leaf superlatives two leaf superlatives the first card is triple auto bob macadoo dr jay and magic johnson four of eight there you go tom congrats buddy that's actually nasty triple auto of three uh nba 75th players very cool that's mvp macadoo 74 75 dr j 80 81 and magic 86 7 nice one there tom congrats buddy that is a the goat griffy jerry rice steve curry leonel messy 19 of 20 congrats on that one i don't believe so no fresh hell yeah man that's awesome that's tom the goats griffy rice curry and messy that is for sure the goats you got something here oh that might be a cleat oh is it okay because there was a people on the cleat that was like that that's kind of sick actually so it might be something crazy along those lines yeah all right well we'll start here with a uh floyd mayweather 205 money 205 crats on that one there uh that's awesome congrats there uh tom and then we've got chris bryant spectacular spikes game use cleat card kb wow that's actually really insane that's so cool well congrats on that tom that is game use from superlative wow insane dude insane that'll do it for your break there tom thanks again for the support buddy um we'll get them right out to you my friend uh guys i think i'm gonna go ahead i gotta call personals now i've got a few things i have to do on the back end here um there's only a couple orders left and kyle will be able to get to him tomorrow so i do apologize on that i got a couple things i gotta take care of so i'm gonna go ahead and do that now um so i appreciate that everybody thank you timmy appreciate that man okay so you've got uh here is your link to the break schedule again you'll have uh forest and matt tomorrow morning matt on or forest on main channel matt on channel two uh you will have me at night on the main channel doing group breaks and then kyle on channel two doing personal so thank you all i appreciate that like i said i got a couple things i gotta get done here i just want to make sure it all gets done right especially for the um the national promo it's the last day of the national promo i want to make sure everything gets uh over there safely so thank you all again i will see you guys again tomorrow night


Hello Earth citizens! In this video I will guide a 10 minute routine on how to open up your sixth chakra. The sixth chakra, also known as the third eye chakra, is located here in the middle of your forehead in between your eyebrows and it governs your intuition, your wisdom, and your mental clarity. If you feel like you have brain fog or you don't have mental clarity, you can't think straight, you can't make decisions straight, then these exercises could be great for unblocking the sixth chakra and helping you focus and gain more mental clarity into your situation.  Great job! Now let's find our sixth chakra.  Now you can lower your hand and feel your sixth chakra, feel the sensations on your forehead, you may feel a tingling sensation, you may feel heat, focus and bring your awareness to your sixth chakra.  Now imagine yourself on that screen, imagine yourself healthy, happy and peaceful, imagine yourself on that screen achieving something that you needed clarity in, making a decision in something that you needed helping.  Now raise your palms up, up to your sixth chakra and your brain.   Right, great job. Now lower your palms and repeat after me either in your mind or out loud. I am wise. I am intuitive. My mind is clear. My brain is clear. I can make decisions. I can do it. I will do it. I am wise. I am intuitive. My mind is clear. My brain is clear. I can make decisions. I can do it. I will do it. Okay, great job.  Deep breath in through your nose.  One more time. Deep breath in through your nose.  Okay, now open your eyes and let's sweep down, sweep down our bodies.  Wake up, rub your arms together, rub your palms together, and sweep down, sweep down everywhere. Sweep, sweep. Great job. So how do you feel?  Do you feel like you can make decisions? Do you feel like your brain fog has lifted away? Please write your experiences in the comment section below. I hope this meditation helped you. Thank you so much for joining and if you're interested in a one-hour brain education-based class, please visit a local Body and Brain yoga studio near you.