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    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?

    © BrainMass Inc. brainmass.com October 9, 2019, 8:29 pm ad1c9bdddf
    https://brainmass.com/math/discrete-math/bijection-proof-152435

    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.

    $2.19