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Math Help - Subsets of compact spaces

  1. #1
    Senior Member I-Think's Avatar
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    Subsets of compact spaces

    Can anyone provide me with an example of a compact space that has subsets that aren't compact?
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  2. #2
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    Re: Subsets of compact spaces

    Quote Originally Posted by I-Think View Post
    Can anyone provide me with an example of a compact space that has subsets that aren't compact?
    Any compact subset of a Hausdorff space with the relative topology is a compact space.
    Now any open set is that compact subspace is not compact. WHY?

    Example: [-2,2]\subset \mathbb{R}^1 with the relative topology is a compact space.

    But (0,1) is not compact.
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