Is this claim true? Assume that [itex]X,Y[/itex] are topological spaces, and that all closed subsets of [itex]X[/itex] are compact. Then all continuous bijections [itex]f:X\to Y[/itex] are homeomorphisms.(adsbygoogle = window.adsbygoogle || []).push({});

It looks true on my notebook, but I don't have a reference, and I don't trust my skills. Just checking.

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# From continuity to homeomorphism, compactness in domain

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