Explore BrainMass

Explore BrainMass

    Bijection Proof

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    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.