
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 nonabsolutely $H$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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MSC: 22A05, 22A15, 22A26; 20M18, 20M15 Received: 17.09.2014 Revised: 17.09.2014
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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 5985
\mathnet{http://mi.mathnet.ru/adm482}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=3280257}
\zmath{https://zbmath.org/?q=an:1315.22004}
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This publication is cited in the following articles:

Serhii Bardyla, Oleg Gutik, “On a semitopological polycyclic monoid”, Algebra Discrete Math., 21:2 (2016), 163–183

S. Bardyla, O. Gutik, A. Ravsky, “Hclosed quasitopological groups”, Topology Appl., 217 (2017), 51–58

T. Banakh, “Categorically closed topological groups”, Axioms, 6:3 (2017), 23

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