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Q: Proper map induced from a continuous map

AmorFatiConsider the following claim. Claim: Let $X$ and $Y$ be locally compact topological spaces, and $f : X \longrightarrow Y$ a continuous map. Suppose that $W \subset X$ is a relatively compact set. Then the induced map (obtained by restricting $f$) $$f : W \backslash f^{-1}(f(\partial W)) \longrig...

 

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