10 Prove that a topological space is compact it and only it every ultra-
filter in it is convergent.​

Question

10 Prove that a topological space is compact it and only it every ultra-
filter in it is convergent.​

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Serenity 2 months 2021-07-27T14:51:04+00:00 2 Answers 0 views 0

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    0
    2021-07-27T14:52:16+00:00

    A topological space X is compact if and only if every ultrafilter in X is convergent. α1 ∩ททท∩ U c αn = (Uα1 ∪ททท∪ Uαn )c = ∅. … Let X be a topological space. A family B of open subsets of X is a basis for the topology of X if every open subset of X is a union of elements of B, explicitly: (1) Every U ∈ B is an open set.

    0
    2021-07-27T14:52:28+00:00

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    A topological space X is compact if and only if every ultrafilter in X is convergent. α1 ∩ททท∩ U c αn = (Uα1 ∪ททท∪ Uαn )c = ∅. … Let X be a topological space. A family B of open subsets of X is a basis for the topology of X if every open subset of X is a union of elements of B, explicitly: (1) Every U ∈ B is an open set.

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