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...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2003 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2003
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155719 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862553955622453248 |
|---|---|
| author | Banakh, T. Ravsky, S. |
| author_facet | Banakh, T. Ravsky, S. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-11-25T21:28:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155719 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T21:28:45Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Banakh, T. Ravsky, S. 2019-06-17T11:14:56Z 2019-06-17T11:14:56Z 2003 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. https://nasplib.isofts.kiev.ua/handle/123456789/155719 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. The first author was supported in part by the Slovenian-Ukrainian research grant
 SLO-UKR 02-03/04. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On subgroups of saturated or totally bounded paratopological groups Article published earlier |
| spellingShingle | On subgroups of saturated or totally bounded paratopological groups Banakh, T. Ravsky, S. |
| title | 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_short | On subgroups of saturated or totally bounded paratopological groups |
| title_sort | on subgroups of saturated or totally bounded paratopological groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155719 |
| work_keys_str_mv | AT banakht onsubgroupsofsaturatedortotallyboundedparatopologicalgroups AT ravskys onsubgroupsofsaturatedortotallyboundedparatopologicalgroups |