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Algebra and Discrete Mathematics, 2003, Issue 4, Pages 1–20
(Mi adm389)
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This article is cited in 9 scientific papers (total in 9 papers)
RESEARCH ARTICLE
On subgroups of saturated or totally bounded paratopological groups
Taras Banakhab, Sasha Ravskyb a Instytut Matematyki, Akademia
Świętokrzyska in Kielce, Świętokrzyska 15, Kielce, 25406, Poland
b Department of Mathematics, Ivan Franko
Lviv National University, Universytetska, 1
Lviv, 79000, Ukraine
Abstract:
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.
Keywords:
saturated paratopological group, group reflexion.
Citation:
Taras Banakh, Sasha Ravsky, “On subgroups of saturated or totally bounded paratopological groups”, Algebra Discrete Math., 2003, no. 4, 1–20
Linking options:
https://www.mathnet.ru/eng/adm389 https://www.mathnet.ru/eng/adm/y2003/i4/p1
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Abstract page: | 181 | Full-text PDF : | 121 | First page: | 1 |
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