On subgroups of saturated or totally bounded paratopological groups
A paratopological group \(G\) is saturated if the inverse \(U^{-1}\) of each non-empty set \(U\subset G\) has non-empty interior. It is shown that a [first-countable] paratopological group \(H\) is a closed subgroup of a saturated (totally bounded) [abelian] paratopological group if and only if \(H\...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/969 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9692018-05-14T07:18:11Z On subgroups of saturated or totally bounded paratopological groups Banakh, Taras Ravsky, Sasha saturated paratopological group, group reflexion 22A15, 54H10, 54H11 A paratopological group \(G\) is saturated if the inverse \(U^{-1}\) of each non-empty set \(U\subset G\) has non-empty interior. It is shown that a [first-countable] paratopological group \(H\) is a closed subgroup of a saturated (totally bounded) [abelian] paratopological group if and only if \(H\) admits a continuous bijective homomorphism onto a (totally bounded) [abelian] topological group \(G\) [such that for each neighborhood \(U\subset H\) of the unit \(e\) there is a closed subset \(F\subset G\) with \(e\in h^{-1}(F)\subset U\)]. As an application we construct a paratopological group whose character exceeds its \(\pi\)-weight as well as the character of its group reflexion. Also we present several examples of (para)topological groups which are subgroups of totally bounded paratopological groups but fail to be subgroups of regular totally bounded paratopological groups. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/969 Algebra and Discrete Mathematics; Vol 2, No 4 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/969/498 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
saturated paratopological group group reflexion 22A15 54H10 54H11 |
| spellingShingle |
saturated paratopological group group reflexion 22A15 54H10 54H11 Banakh, Taras Ravsky, Sasha On subgroups of saturated or totally bounded paratopological groups |
| topic_facet |
saturated paratopological group group reflexion 22A15 54H10 54H11 |
| format |
Article |
| author |
Banakh, Taras Ravsky, Sasha |
| author_facet |
Banakh, Taras Ravsky, Sasha |
| author_sort |
Banakh, Taras |
| title |
On subgroups of saturated or totally bounded paratopological groups |
| title_short |
On subgroups of saturated or totally bounded paratopological groups |
| title_full |
On subgroups of saturated or totally bounded paratopological groups |
| title_fullStr |
On subgroups of saturated or totally bounded paratopological groups |
| title_full_unstemmed |
On subgroups of saturated or totally bounded paratopological groups |
| title_sort |
on subgroups of saturated or totally bounded paratopological groups |
| description |
A paratopological group \(G\) is saturated if the inverse \(U^{-1}\) of each non-empty set \(U\subset G\) has non-empty interior. It is shown that a [first-countable] paratopological group \(H\) is a closed subgroup of a saturated (totally bounded) [abelian] paratopological group if and only if \(H\) admits a continuous bijective homomorphism onto a (totally bounded) [abelian] topological group \(G\) [such that for each neighborhood \(U\subset H\) of the unit \(e\) there is a closed subset \(F\subset G\) with \(e\in h^{-1}(F)\subset U\)]. As an application we construct a paratopological group whose character exceeds its \(\pi\)-weight as well as the character of its group reflexion. Also we present several examples of (para)topological groups which are subgroups of totally bounded paratopological groups but fail to be subgroups of regular totally bounded paratopological groups. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/969 |
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AT banakhtaras onsubgroupsofsaturatedortotallyboundedparatopologicalgroups AT ravskysasha onsubgroupsofsaturatedortotallyboundedparatopologicalgroups |
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2024-04-12T06:25:57Z |
| last_indexed |
2024-04-12T06:25:57Z |
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1796109214522802176 |