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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/153347 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862531548104884224 |
|---|---|
| author | Gutik, O. |
| author_facet | Gutik, O. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-24T04:41:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153347 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-24T04:41:49Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Gutik, O. 2019-06-14T03:26:11Z 2019-06-14T03:26:11Z 2014 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. https://nasplib.isofts.kiev.ua/handle/123456789/153347 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. The author acknowledges Oleksandr Ravskyi for his comments and suggestions. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On closures in semitopological inverse semigroups with continuous inversion Article published earlier |
| spellingShingle | On closures in semitopological inverse semigroups with continuous inversion Gutik, O. |
| title | 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_short | On closures in semitopological inverse semigroups with continuous inversion |
| title_sort | on closures in semitopological inverse semigroups with continuous inversion |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153347 |
| work_keys_str_mv | AT gutiko onclosuresinsemitopologicalinversesemigroupswithcontinuousinversion |