Can one construct homeomorphism between (-1,1)×[-1,1) and [-1,1]×[-1,1)? If so, please show me how to construct it.
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3$\begingroup$ Why have you posted the same question twice? $\endgroup$– Gerry MyersonCommented Feb 2, 2016 at 11:46
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4$\begingroup$ This does not look research level to me. $\endgroup$– Lev BorisovCommented Feb 2, 2016 at 11:54
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1 Answer
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I think it is pretty easy to construct a homeomorphism, but very hard to describe. Therefore, I attached an image (consider the red lines as closed and the gray as open).
The first homeomorphism just makes the square round and in the second you stretch and compress the radial directions. The third is the inverse of the first.
Of course my draws are horrible and nothing is in the right scale, but I hope you got the idea.
In any case, it is really a homework.
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1$\begingroup$ I wouldn't say "very hard to describe", there's a nice PL map, triangulating both squares into six triangles ;) $\endgroup$ Commented Feb 2, 2016 at 13:21
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$\begingroup$ @AchimKrause: Indeed :) But I am worst in writting then in drawing $\endgroup$– LlohannCommented Feb 2, 2016 at 13:58
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3$\begingroup$ Please do not answer off-topic questions. It is, as you say, homework-level (for an undergraduate course in topology). $\endgroup$ Commented Feb 2, 2016 at 14:04
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1$\begingroup$ I will ask no more question forever. $\endgroup$– yutaCommented Feb 2, 2016 at 14:37
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2$\begingroup$ We are not passing judgement on you, just on your question. If you have actual research questions in the future, this may well be the site for them. $\endgroup$ Commented Feb 2, 2016 at 14:42