On \(H\)-closed topological semigroups and semilattices
In this paper, we show that if \(S\) is an \(H\)-closed topological semigroup and \(e\) is an idempotent of \(S\), then \(eSe\) is an \(H\)-closed topological semigroup. We give sufficient conditions on a linearly ordered topological semilattice to be \(H\)-closed. Also we prove that any \(H\)-close...
Gespeichert in:
| Datum: | 2018 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/831 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | In this paper, we show that if \(S\) is an \(H\)-closed topological semigroup and \(e\) is an idempotent of \(S\), then \(eSe\) is an \(H\)-closed topological semigroup. We give sufficient conditions on a linearly ordered topological semilattice to be \(H\)-closed. Also we prove that any \(H\)-closed locally compact topological semilattice and any \(H\)-closed topological weakly \(U\)-semilattice contain minimal idempotents. An example of a countably compact topological semilattice whose topological space is \(H\)-closed is constructed. |
|---|