Bijection Proof
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Let f : M -> N be a continuous bijection. M is compact.
Show that f is a homeomorphism.
Isn't a homeomorphism by definition a bijection? And since M is compact, will it not be true that N will be compact too?
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Solution Summary
This is a proof regarding bijection and homemorphism.
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yes, homeomorphisms are bijections by definition alone;
and since M is compact, f(M) = N is compact as well
to prove the claim, you also want N to be Hausdorff
in that ...
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