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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

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

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
Revised: 17.09.2014
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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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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
2. S. Bardyla, O. Gutik, A. Ravsky, “H-closed quasitopological groups”, Topology Appl., 217 (2017), 51–58
3. T. Banakh, “Categorically closed topological groups”, Axioms, 6:3 (2017), 23
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