Counting topologies (Q550543)
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scientific article; zbMATH DE number 5919430
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counting topologies |
scientific article; zbMATH DE number 5919430 |
Statements
Counting topologies (English)
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12 July 2011
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For an infinite set \(X\), the author computes the number of topologies on \(X\) which are \(P\), where \(P\) is some combination of compact (without \(T_2\)), connected, \(T_1\), \(T_2\), \(T_4\), \(T_5\). E.g. he shows that this number is \(2^{2^{|X|}}\) if \(P\) is connected ore compact ore \(T_2\), but only \(2^{|X|}\) if \(P\) is compact and \(T_2\) (\(|X|\) is the cardinal number of \(X\)).
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(connected, compact, \(T_1\), \(T_2\), \(T_4\), \(T_5\)) toplogical space
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cardinality
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ultrafilter
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