Let $X$ and $Y$ be two spaces which are homeomorphic. If one of them is compact, how do I show that the other is also compact?
2026-03-28 06:48:36.1774680516
How do I show that the set is compact?
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Because if $X$ is compact and $f\colon X\longrightarrow Y$ is continuous, then $f(X)$ is compact.