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Thread: sequential compactness

  1. May 11th 2010, 08:36 AM #1
    Alex314
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    sequential compactness

    How do you prove the following theorem?
    If X is a metric space and E a subset of X is compact, then E is sequentially compact.
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  2. May 11th 2010, 08:56 AM #2
    Plato
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    Quote Originally Posted by Alex314 View Post
    How do you prove the following theorem?
    If X is a metric space and E a subset of X is compact, then E is sequentially compact.
    Is it possible that there is an infinite subset of E with no accumulation point in X?
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