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Math Help - topology on three point set?

  1. #1
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    topology on three point set?

    Let X = {a,b,c}
    Construct a topology on X so that there is a compact set that is not closed.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by iamthemanyes View Post
    Let X = {a,b,c}
    Construct a topology on X so that there is a compact set that is not closed.
    Just make any topology where there is a non-closed set and that non-closed set will be compact since the set if sfinite.
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  3. #3
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    Would this be an example:
    {Zero set, X, {a}, {b,c}, {c}, {a,c}}

    Then {c} is compact, but NOT closed?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by iamthemanyes View Post
    Would this be an example:
    {Zero set, X, {a}, {b,c}, {c}, {a,c}}

    Then {c} is compact, but NOT closed?
    Right.
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