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.

**Physics Forums - The Fusion of Science and Community**

# From continuity to homeomorphism, compactness in domain

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

Have something to add?

- Similar discussions for: From continuity to homeomorphism, compactness in domain

Loading...

**Physics Forums - The Fusion of Science and Community**