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Does there exist a continuous open function $f:B^n\to B^n$ which is not injective? (Here $B^n\subseteq\mathbb{R}^n$ is the open unit ball)

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  • $\begingroup$ What is an open function? $\endgroup$ – enzotib Jul 29 '12 at 16:12
  • $\begingroup$ @enzotib: It's a function that maps open sets to open sets. (See http://en.wikipedia.org/wiki/Open_and_closed_maps.) $\endgroup$ – ruakh Jul 29 '12 at 16:13
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    $\begingroup$ Do you want the function to be surjective? Otherwise the question is not much fun. $\endgroup$ – Henning Makholm Jul 29 '12 at 16:20
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    $\begingroup$ is this map works? $re^{ix}\mapsto re^{2ix}$? $\endgroup$ – Marso Jul 29 '12 at 16:27
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    $\begingroup$ @carizio: Please don't delete your question just because you get a satisfactory answer. Doing so deprives the answerer of the chance to earn reputation, and deprives future vistors to the site of the chance to learn from the question and its answer. $\endgroup$ – Henning Makholm Jul 29 '12 at 16:54
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Hint for your problem: $re^{ix}\mapsto re^{2ix}$.

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