$On $H$-closed topological semigroups and semilattices$

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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Date:	2018
Main Authors:	Chuchman, Ivan, Gutik, Oleg
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2018
Subjects:	Topological semigroup $H$-closed topological semigroup absolutely $H$-closed topological semigroup topological semilattice linearly ordered semilattice $H$-closed topological semilattice absolutely $H$-closed topological semilattice 06A12 06F30; 22A15 22A26 54H12
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/831
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Journal Title:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-831
record_format	ojs
spelling	admjournalluguniveduua-article-8312018-03-21T11:52:32Z On $H$-closed topological semigroups and semilattices Chuchman, Ivan Gutik, Oleg Topological semigroup, $H$-closed topological semigroup, absolutely $H$-closed topological semigroup, topological semilattice, linearly ordered semilattice, $H$-closed topological semilattice, absolutely $H$-closed topological semilattice 06A12, 06F30; 22A15, 22A26, 54H12 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/831 Algebra and Discrete Mathematics; Vol 6, No 1 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/831/362 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-03-21T11:52:32Z
collection	OJS
language	English
topic	Topological semigroup $H$-closed topological semigroup absolutely $H$-closed topological semigroup topological semilattice linearly ordered semilattice $H$-closed topological semilattice absolutely $H$-closed topological semilattice 06A12 06F30; 22A15 22A26 54H12
spellingShingle	Topological semigroup $H$-closed topological semigroup absolutely $H$-closed topological semigroup topological semilattice linearly ordered semilattice $H$-closed topological semilattice absolutely $H$-closed topological semilattice 06A12 06F30; 22A15 22A26 54H12 Chuchman, Ivan Gutik, Oleg On $H$-closed topological semigroups and semilattices
topic_facet	Topological semigroup $H$-closed topological semigroup absolutely $H$-closed topological semigroup topological semilattice linearly ordered semilattice $H$-closed topological semilattice absolutely $H$-closed topological semilattice 06A12 06F30; 22A15 22A26 54H12
format	Article
author	Chuchman, Ivan Gutik, Oleg
author_facet	Chuchman, Ivan Gutik, Oleg
author_sort	Chuchman, Ivan
title	On $H$-closed topological semigroups and semilattices
title_short	On $H$-closed topological semigroups and semilattices
title_full	On $H$-closed topological semigroups and semilattices
title_fullStr	On $H$-closed topological semigroups and semilattices
title_full_unstemmed	On $H$-closed topological semigroups and semilattices
title_sort	on $h$-closed topological semigroups and semilattices
description	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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/831
work_keys_str_mv	AT chuchmanivan onhclosedtopologicalsemigroupsandsemilattices AT gutikoleg onhclosedtopologicalsemigroupsandsemilattices
first_indexed	2025-12-02T15:37:14Z
last_indexed	2025-12-02T15:37:14Z
_version_	1850411407954149376

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

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