For $n \ge 2$ give example of a bijective continuous map $f: \mathbb R^n \to \mathbb R^n$ whose inverse is not continuous ; example of such a function is also an example of Does there exist a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?


marked as duplicate by Gerry Myerson, Najib Idrissi, AlexR, drhab, Did Oct 6 '14 at 9:11

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    $\begingroup$ There is no such function due to "invariance of domain". en.m.wikipedia.org/wiki/Invariance_of_domain $\endgroup$ – PhoemueX Oct 6 '14 at 4:53
  • $\begingroup$ @PhoemueX: what is "invariance of domain" ?? $\endgroup$ – Souvik Dey Oct 6 '14 at 4:54
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    $\begingroup$ I edited my comment and provided a link. It is a theorem telling you that an injective continuous map $f : U \to \Bbb{R}^n$ with $U \subset \Bbb{R}^n$ open is always an open map, so that the inverse is also continuous. $\endgroup$ – PhoemueX Oct 6 '14 at 4:56