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Math Help - Homeomorphism

  1. #1
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    Homeomorphism

    Dear Colleagues,

    Let X and Y be metric spaces, X compact, and T:X\longrightarrow Y bijective and continuous. Show that T is a homeomorphism i.e. T^{-1} is continuous.

    Could you please help me in solving this problem.


    Regards,

    Raed.
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  2. #2
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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.
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  3. #3
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    Thank you very much for your reply.
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