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Math Help - Converhence

  1. #1
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    Converhence

    Let (an) be a sequence in X, (that is for al n in N, an in X) such that the set of the sequence, {an:n in N}, is infinite.

    Using the definition of a convergence in topological spaces, prove that (an) has a subsequence which converges to p.

    Note that X is an infinite and p a point in X chosen once and for all. Let T be the collection of subsets of V of Xfor which either p is NOT a member of V, or p in V, AND its compliment is finite.

    A proof please?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Cairo View Post
    Let (an) be a sequence in X, (that is for al n in N, an in X) such that the set of the sequence, {an:n in N}, is infinite.

    Using the definition of a convergence in topological spaces, prove that (an) has a subsequence which converges to p.

    Note that X is an infinite and p a point in X chosen once and for all. Let T be the collection of subsets of V of Xfor which either p is NOT a member of V, or p in V, AND its compliment is finite.

    A proof please?
    Maybe someone else can understand this. But, I can't.
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