Let me consider a continuous function $y=f(x)$ for $x \in [0,1]$. Now consider its inverse $f^{-1}(y)= \{x:f(x)=y \}$. How can I characterize continuity property of $f^{-1}(y)$ in terms of $y$?
Continuity of inverse mapping of a continuous function
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real-analysis
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0Yes but I meant some property of $f^{-1}$ as a correspondence. – 2011-03-27
1 Answers
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Well, benyond being bijective, $f$ must send open sets to open sets.
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0@Thales Assuming $f^{-1}$ continous, yes. – 2011-03-28