Thread: Homeomorphism

Dear Colleagues,

Let and be metric spaces, compact, and bijective and continuous. Show that is a homeomorphism i.e. is continuous.

Could you please help me in solving this problem.


Regards,

Raed.

A proof from Munkres "Topology" 2nd edition, page 167 is shown in the image below. Note that a metric space is normal (Th 32.2 in P202 of this textbook) and therefore Hausdorff.

Thank you very much for your reply.