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  3. let (x,dx),(y,dy ) be metric spaces and f: x ? y b

Let (X,dX),(Y,dY ) be metric spaces and f: X ? Y be a continuous bijection. Prove...

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Advance Math

Let (X,dX),(Y,dY ) be metric spaces and f: X ? Y be a continuousbijection. Prove that if (X, dX ) is compact, then f is ahomeomorphism. (Hint: it might be convenient to use that a functionis continuous if and only if the inverse image of every open set isopen, if and only if the inverse image of every closed set isclosed).

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