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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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    @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.2012-07-29

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Hint for your problem: $re^{ix}\mapsto re^{2ix}$.