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Math Help - Local Compactness

  1. #1
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    Local Compactness

    Dear Colleagues,

    A metric space X is said to be locally compact if every point of X has a compact neighborhood. Show that a compact metric space X is locally compact.


    Regards,

    Raed.
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  2. #2
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    Quote Originally Posted by raed View Post
    Dear Colleagues,

    A metric space X is said to be locally compact if every point of X has a compact neighborhood. Show that a compact metric space X is locally compact.


    Regards,

    Raed.

    X is a neighborhood of each and every point in it, so...

    Tonio
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    For every p\in X , X is a compact neighbourhood of p .


    Edited: Sorry, I didn't see the previous answer.
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  4. #4
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    Thank you very much.
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