Let $f_n$ be a sequence of continuous function such that $f_n \rightarrow f$ uniformly on compact sets. In addition both $f_n$ and $f$ are continuous. Then do we have $f^{-1}_n \rightarrow f^{-1}$ pointwise? If so do we have uniform convergence?
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2Is some of the "continuous" supposed to be "bijective" (or "injective and surjective onto a common set")? – Mar 02 '20 at 14:16
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1Assuming the functions are bijective (so that the inverses exist), the answer is yes. See https://math.stackexchange.com/questions/1106324/convergence-of-a-sequence-of-functions-and-their-inverses – Prasiortle Mar 02 '20 at 14:24
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@Prasiortle your link is not working, it redirects to this same page – qwertyguy Mar 02 '20 at 14:25
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1@qwertyguy I have fixed the link now. – Prasiortle Mar 02 '20 at 14:26
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Does this answer your question? Convergence of a sequence of functions and their inverses – Anne Bauval Feb 27 '24 at 11:32
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What is the context ($\Bbb R$? metric spaces? general topological spaces?) and what were your attempts? Please do not answer in comment. Edit your post. Quick beginner guide for asking a well-received question + please avoid "no clue" questions. – Anne Bauval Feb 27 '24 at 11:36