Take the tour ×  Cam anyone provide me the proof of:  that
$\mathbb{R}^{2}\setminus (\mathbb{Q}\times \mathbb{Q}) \subset
\mathbb{R}^{2}$ is connected.  share|improve this question
Ideally you should say what you tried. Hint: you could try
showing it is path connected. –  Matt Pressland May 16 '12 at
16:19 This is answered in
math.stackexchange.com/questions/16948/… in both the comments
(by Jacob Schlather) and as an actual answer (by Jeremy
Hurwitz.) The questions, themselves, are different, so I'm not
sure if this should be closed as a duplicate or not. –  Jason
DeVito May 16 '12 at 16:21 I would suggest this question should
be left open, as it's far more likely to come up in a search
related to this problem. –  Matt Pressland May 16 '12 at 16:37
Michael Hardy's solution seems clear to me, but if for some
reason you don't get it you might prefer to consider why
$\mathbb{R}\setminus(\mathbb{Z}\times\mathbb{Z})$ is connected;
it might be easier to visualize. –  MJD May 16 '12 at 17:12
Another near duplicate?