On closures in semitopological inverse semigroups with continuous inversion

• Datum: 2018
• 1. Verfasser: Gutik, Oleg
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: semigroup; semitopological semigroup; topological Brandt \(\lambda^0\)-extension; inverse semigroup; quasitopological group; topological group; semilattice; closure; \(H\)-closed; absolutely \(H\)-closed; 22A05; 22A15; 22A26; 20M18; 20M15
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1047
• Назва журналу: Algebra and Discrete Mathematics

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.