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Algebra Discrete Math., 2014, Volume 18, Issue 1, Pages 59–85 (Mi adm482)  

This article is cited in 3 scientific papers (total in 3 papers)

RESEARCH ARTICLE

On closures in semitopological inverse semigroups with continuous inversion

Oleg Gutik

Faculty of Mechanics and Mathematics, National University of Lviv, Universytetska 1, Lviv, 79000, Ukraine

Abstract: 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.

Keywords: semigroup, semitopological semigroup, topological Brandt $\lambda^0$-extension, inverse semigroup, quasitopological group, topological group, semilattice, closure, $H$-closed, absolutely $H$-closed.

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Bibliographic databases:
MSC: 22A05, 22A15, 22A26; 20M18, 20M15
Received: 17.09.2014
Revised: 17.09.2014
Language:

Citation: Oleg Gutik, “On closures in semitopological inverse semigroups with continuous inversion”, Algebra Discrete Math., 18:1 (2014), 59–85

Citation in format AMSBIB
\Bibitem{Gut14}
\by Oleg~Gutik
\paper On closures in semitopological inverse semigroups with continuous inversion
\jour Algebra Discrete Math.
\yr 2014
\vol 18
\issue 1
\pages 59--85
\mathnet{http://mi.mathnet.ru/adm482}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3280257}
\zmath{https://zbmath.org/?q=an:1315.22004}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Serhii Bardyla, Oleg Gutik, “On a semitopological polycyclic monoid”, Algebra Discrete Math., 21:2 (2016), 163–183  mathnet  mathscinet
    2. S. Bardyla, O. Gutik, A. Ravsky, “H-closed quasitopological groups”, Topology Appl., 217 (2017), 51–58  crossref  mathscinet  zmath  isi  scopus
    3. T. Banakh, “Categorically closed topological groups”, Axioms, 6:3 (2017), 23  crossref  isi  scopus
  • Algebra and Discrete Mathematics
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