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
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 ...
This is a proof regarding bijection and homemorphism.