2
$\begingroup$

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 $y$?

  • 0
    Yes but I meant some property of $f^{-1}$ as a correspondence.2011-03-27

1 Answers 1

0

Well, benyond being bijective, $f$ must send open sets to open sets.

  • 0
    @Thales Assuming $f^{-1}$ continous, yes.2011-03-28