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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1047 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
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AT gutikoleg onclosuresinsemitopologicalinversesemigroupswithcontinuousinversion |
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2025-07-17T10:34:09Z |
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2025-07-17T10:34:09Z |
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1837889958802620416 |