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.
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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.
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