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 ⊂ 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 b...
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| Дата: | 2003 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155719 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On subgroups of saturated or totally bounded paratopological groups / T. Banakh, S. Ravsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 1–20. — Бібліогр.: 25 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1557192019-06-18T01:27:26Z On subgroups of saturated or totally bounded paratopological groups Banakh, T. Ravsky, S. A paratopological group G is saturated if the inverse U ⁻¹ of each non-empty set U ⊂ 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 ⊂ H of the unit e there is a closed subset F ⊂ G with e ∈ h ⁻¹ (F) ⊂ U]. As an application we construct a paratopological group whose character exceeds its π-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. 2003 Article On subgroups of saturated or totally bounded paratopological groups / T. Banakh, S. Ravsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 1–20. — Бібліогр.: 25 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 22A15, 54H10, 54H11. http://dspace.nbuv.gov.ua/handle/123456789/155719 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 |
A paratopological group G is saturated if the inverse U
⁻¹ of each non-empty set U ⊂ 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 ⊂ H of the unit e there is a closed subset
F ⊂ G with e ∈ h
⁻¹
(F) ⊂ U]. As an application we construct a
paratopological group whose character exceeds its π-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. |
| format |
Article |
| author |
Banakh, T. Ravsky, S. |
| spellingShingle |
Banakh, T. Ravsky, S. On subgroups of saturated or totally bounded paratopological groups Algebra and Discrete Mathematics |
| author_facet |
Banakh, T. Ravsky, S. |
| author_sort |
Banakh, T. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155719 |
| citation_txt |
On subgroups of saturated or totally bounded paratopological groups / T. Banakh, S. Ravsky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 1–20. — Бібліогр.: 25 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT banakht onsubgroupsofsaturatedortotallyboundedparatopologicalgroups AT ravskys onsubgroupsofsaturatedortotallyboundedparatopologicalgroups |
| first_indexed |
2023-05-20T17:47:05Z |
| last_indexed |
2023-05-20T17:47:05Z |
| _version_ |
1796154078811652096 |