Эта публикация цитируется в
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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
Аннотация:
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.
Ключевые слова:
semigroup, semitopological semigroup, topological Brandt
$\lambda^0$-extension, inverse semigroup, quasitopological group, topological group, semilattice, closure,
$H$-closed, absolutely
$H$-closed.
MSC: 22A05,
22A15,
22A26;
20M18,
20M15 Поступила в редакцию: 17.09.2014
Исправленный вариант: 17.09.2014
Язык публикации: английский