On closures in semitopological inverse semigroups with continuous inversion
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...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2014
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153347 |
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| Цитувати: | On closures in semitopological inverse semigroups with continuous inversion / O. Gutik // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 59–85. — Бібліогр.: 33 назв. — англ. |
Репозиторії
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irk-123456789-1533472019-06-15T01:30:35Z On closures in semitopological inverse semigroups with continuous inversion Gutik, O. 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 λ⁰-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. 2014 Article On closures in semitopological inverse semigroups with continuous inversion / O. Gutik // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 59–85. — Бібліогр.: 33 назв. — англ. 1726-3255 2010 MSC:22A05, 22A15, 22A26; 20M18, 20M15. http://dspace.nbuv.gov.ua/handle/123456789/153347 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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 λ⁰-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. |
| format |
Article |
| author |
Gutik, O. |
| spellingShingle |
Gutik, O. On closures in semitopological inverse semigroups with continuous inversion Algebra and Discrete Mathematics |
| author_facet |
Gutik, O. |
| author_sort |
Gutik, O. |
| title |
On closures in semitopological inverse semigroups with continuous inversion |
| title_short |
On closures in semitopological inverse semigroups with continuous inversion |
| title_full |
On closures in semitopological inverse semigroups with continuous inversion |
| title_fullStr |
On closures in semitopological inverse semigroups with continuous inversion |
| title_full_unstemmed |
On closures in semitopological inverse semigroups with continuous inversion |
| title_sort |
on closures in semitopological inverse semigroups with continuous inversion |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153347 |
| citation_txt |
On closures in semitopological inverse semigroups with continuous inversion / O. Gutik // Algebra and Discrete Mathematics. — 2014. — Vol. 18, № 1. — С. 59–85. — Бібліогр.: 33 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:38:31Z |
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