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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Datum:2003
Hauptverfasser: Banakh, T., Ravsky, S.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2003
Schriftenreihe:Algebra and Discrete Mathematics
Online Zugang: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
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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spelling 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
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first_indexed 2025-07-14T07:55:54Z
last_indexed 2025-07-14T07:55:54Z
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