On closures in semitopological inverse semigroups with continuous inversion

We study the closures of subgroups, semilattices and different kinds of semigroup extensions in semitopological inverse semigroups with continuous inversion. In particularly we show that a topological group \(G\) is \(H\)-closed in the class of semitopological inverse semigroups with continuous inve...

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Date:	2018
Main Author:	Gutik, Oleg
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	semigroup semitopological semigroup topological Brandt \(\lambda^0\)-extension inverse semigroup quasitopological group topological group semilattice closure \(H\)-closed absolutely \(H\)-closed 22A05 22A15 22A26; 20M18 20M15
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1047
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Journal Title:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-1047
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spelling	admjournalluguniveduua-article-10472018-04-26T02:28:53Z On closures in semitopological inverse semigroups with continuous inversion Gutik, Oleg semigroup, semitopological semigroup, topological Brandt \(\lambda^0\)-extension, inverse semigroup, quasitopological group, topological group, semilattice, closure, \(H\)-closed, absolutely \(H\)-closed 22A05, 22A15, 22A26; 20M18, 20M15 We study the closures of subgroups, semilattices and different kinds of semigroup extensions in semitopological inverse semigroups with continuous inversion. In particularly we show that a topological group \(G\) is \(H\)-closed in the class of semitopological inverse semigroups with continuous inversion if and only if \(G\) is compact, a Hausdorff linearly ordered topological semilattice \(E\) is \(H\)-closed in the class of semitopological semilattices if and only if \(E\) is \(H\)-closed in the class of topological semilattices, and a topological Brandt \(\lambda^0\)-extension of \(S\) is (absolutely) \(H\)-closed in the class of semitopological inverse semigroups with continuous inversion if and only if so is \(S\). Also, we construct an example of an \(H\)-closed non-absolutely \(H\)-closed semitopological semilattice in the class of semitopological semilattices. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1047 Algebra and Discrete Mathematics; Vol 18, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1047/569 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-26T02:28:53Z
collection	OJS
language	English
topic	semigroup semitopological semigroup topological Brandt \(\lambda^0\)-extension inverse semigroup quasitopological group topological group semilattice closure \(H\)-closed absolutely \(H\)-closed 22A05 22A15 22A26; 20M18 20M15
spellingShingle	semigroup semitopological semigroup topological Brandt \(\lambda^0\)-extension inverse semigroup quasitopological group topological group semilattice closure \(H\)-closed absolutely \(H\)-closed 22A05 22A15 22A26; 20M18 20M15 Gutik, Oleg On closures in semitopological inverse semigroups with continuous inversion
topic_facet	semigroup semitopological semigroup topological Brandt \(\lambda^0\)-extension inverse semigroup quasitopological group topological group semilattice closure \(H\)-closed absolutely \(H\)-closed 22A05 22A15 22A26; 20M18 20M15
format	Article
author	Gutik, Oleg
author_facet	Gutik, Oleg
author_sort	Gutik, Oleg
title	On closures in semitopological inverse semigroups with continuous inversion
title_short	On closures in semitopological inverse semigroups with continuous inversion
title_full	On closures in semitopological inverse semigroups with continuous inversion
title_fullStr	On closures in semitopological inverse semigroups with continuous inversion
title_full_unstemmed	On closures in semitopological inverse semigroups with continuous inversion
title_sort	on closures in semitopological inverse semigroups with continuous inversion
description	We study the closures of subgroups, semilattices and different kinds of semigroup extensions in semitopological inverse semigroups with continuous inversion. In particularly we show that a topological group \(G\) is \(H\)-closed in the class of semitopological inverse semigroups with continuous inversion if and only if \(G\) is compact, a Hausdorff linearly ordered topological semilattice \(E\) is \(H\)-closed in the class of semitopological semilattices if and only if \(E\) is \(H\)-closed in the class of topological semilattices, and a topological Brandt \(\lambda^0\)-extension of \(S\) is (absolutely) \(H\)-closed in the class of semitopological inverse semigroups with continuous inversion if and only if so is \(S\). Also, we construct an example of an \(H\)-closed non-absolutely \(H\)-closed semitopological semilattice in the class of semitopological semilattices.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1047
work_keys_str_mv	AT gutikoleg onclosuresinsemitopologicalinversesemigroupswithcontinuousinversion
first_indexed	2025-12-02T15:38:14Z
last_indexed	2025-12-02T15:38:14Z
_version_	1850412121093832704

On closures in semitopological inverse semigroups with continuous inversion

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