So i know that an open function is a function with the property that it sends an open interval to an open interval , but how to find a function which is open and not continous ?
Any hints ?
thanks
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In $\Bbb R$ with the usual topology? – Martín-Blas Pérez Pinilla Mar 26 '14 at 08:41
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Do you know how to construct a function $f:\mathbb R\to\mathbb R$ which takes all real values in every interval? – bof Mar 26 '14 at 08:41
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yes in R with usual toplogy – kabary Mar 26 '14 at 08:46
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How about the function $f(z) = \arg z$ mapping from $S_1\subseteq \mathbb C$ to $[0,2\pi)$? An image of every open set is open, but $f$ is not continuous around $1$.
5xum
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