Prove why a closed, continuous bijective map is a homeomorphism. I'm trying to see if $f^{-1}$ is continuous but nothing happens.
2026-02-23 04:37:10.1771821430
Prove why a closed, continuous bijective map is a homeomorphism.
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Theorem. A map $f$ from a metric space $X$ to a metric space $X'$ is continuous iff for every $C$ closed in $X'$ the set $f^{(-1)}(C)$ is closed in $X$.
Can you see now?