On \(H\)-closed topological semigroups and semilattices

In this paper, we show that if \(S\) is an \(H\)-closed topological semigroup and \(e\) is an idempotent of \(S\), then \(eSe\) is an \(H\)-closed topological semigroup. We give sufficient conditions on a linearly ordered topological semilattice to be \(H\)-closed. Also we prove that any \(H\)-close...

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Datum:2018
Hauptverfasser: Chuchman, Ivan, Gutik, Oleg
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/831
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Zusammenfassung:In this paper, we show that if \(S\) is an \(H\)-closed topological semigroup and \(e\) is an idempotent of \(S\), then \(eSe\) is an \(H\)-closed topological semigroup. We give sufficient conditions on a linearly ordered topological semilattice to be \(H\)-closed. Also we prove that any \(H\)-closed locally compact topological semilattice and any \(H\)-closed topological weakly \(U\)-semilattice contain minimal idempotents. An example of a countably compact topological semilattice whose topological space is \(H\)-closed is constructed.