\(K(\beta S)\) is not closed (Q554438)
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scientific article; zbMATH DE number 5935916
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(K(\beta S)\) is not closed |
scientific article; zbMATH DE number 5935916 |
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\(K(\beta S)\) is not closed (English)
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4 August 2011
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Let \(S\) be an infinite semigroup that can algebraically be embedded in a group. It is proved that if the cardinality of \(S\) is not Ulam-measurable, then the smallest two sided ideal \(K(\beta S)\) of the Stone-Čech compactification \(\beta S\) of \(S\) and the set of idempotents from the closure of \(K(\beta S)\) are not closed in \(\beta S\).
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Stone-Čech compactification
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ultrafilter semigroup
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smallest ideal
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idempotents
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