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Thread: Compact sets and covers

  1. #1
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    Compact sets and covers

    If you have a topological space that is compact, is it a cover itself?

    If so, how to prove this?
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  2. #2
    Super Member girdav's Avatar
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    What do you mean by "it is a cover itself" ?
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  3. #3
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    Quote Originally Posted by Borkborkmath View Post
    If you have a topological space that is compact, is it a cover itself?
    If so, how to prove this?
    (X,\mathcal{T}) is a topological space is X a basic open set?
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  4. #4
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    Yeah, sorry for the poor wording.
    I was wondering if (X,tau) was a topological space if X was a cover of (X,tau). Or as plato said.
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  5. #5
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    Quote Originally Posted by Borkborkmath View Post
    Yeah, sorry for the poor wording.
    I was wondering if (X,tau) was a topological space if X was a cover of (X,tau). Or as plato said.
    In any topology space (X,\tau), yes X is an open cover of itself. That fact is true if the space is compact or not compact. So what is the point?
    Please tell us what you are going for.
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  6. #6
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    Just wanted to make sure, thank you :]
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