# Bijection Proof

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 Preview

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 ...

#### Solution Summary

This is a proof regarding bijection and homemorphism.

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