Results 1 to 10 of about 251 (68)
On paratopological groups [PDF]
Topology and its Applications, 2013 In this paper, we firstly construct a Hausdorff non-submetrizable paratopological group $G$ in which every point is a $G_{\delta}$-set, which gives a negative answer to Arhangel'ski\v{\i}\ and Tkachenko's question [Topological Groups and Related ...
Lin, Fucai, Liu, Chuan
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On pseudobounded and premeage paratopological groups
Математичні Студії, 2021 Let $G$ be a paratopological group. Following F.~Lin and S.~Lin, we say that the group $G$ is pseudobounded, if for any neighborhood $U$ of the identity of $G$, there exists a natural number $n$ such that $U^n=G$. The group $G$ is $\omega$-pseudobounded,
A.V. Ravsky, T.O. Banakh
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Applied General Topology, 2015 Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is an Alexandroff
Ali Sayed Elfard
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Characterizing meager paratopological groups
Applied General Topology, 2011 We prove that a Hausdorff paratopological group G is meager if andonly if there are a nowhere dense subset A G and a countable setC G such that CA = G = AC.
Taras Banak, Igor Guran, Alex Ravsky
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Categorically Closed Topological Groups
Axioms, 2017 Let C → be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms.
Taras Banakh
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Group reflection and precompact paratopological groups
Topological Algebra and its Applications, 2013 AbstractWe construct a precompact completely regular paratopological Abelian group G of size (2ω)+ such that all subsets of G of cardinality ≤ 2ω are closed. This shows that Protasov’s theorem on non-closed discrete subsets of precompact topological groups cannot be extended to paratopological groups.
Tkachenko Mikhail
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Cardinal invariants of paratopological groups
Topological Algebra and its Applications, 2013 AbstractWe show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is
Sánchez Iván
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A note on free paratopological groups [PDF]
Topology and its Applications, 2013 In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.Comment: 12 ...
Lin, Fucai
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A note on pseudobounded paratopological groups
Topological Algebra and its Applications, 2014 Let G be a paratopological group. Then G is said to be pseudobounded (resp. ω-pseudobounded) if forevery neighbourhood V of the identity e in G, there exists a natural number n such that G = Vn (resp.we have G = ∪ n∈N Vn).
Lin Fucai, Lin Shou, Sánchez Iván
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The Doitchinov Completion of a Regular Paratopological Group [PDF]
, 1998 In memory of Professor D. Doitchinov ∗ This paper was written while the first author was supported by the Swiss National Science Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry of Education and Sciences under DGES ...
Künzi, Hans-Peter +2 more
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