Results 61 to 70 of about 590 (104)

Axioms of separation in semitopological groups and related functors

Topology and its Applications, 2014
The author considers the category of semitopological groups, that is, groups with a topology in which the left and right translations are continuous; the morphisms of this category are the continuous homomorphisms. No separation assumptions on the topology of the groups are made.
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On some properties of PR (Pm)-factorizable semitopological groups

Filomat
In this article, we introduce the notions of (R?,FM1SG) ((MS,FM1SG))-factorizability and (R?, SCSG) ((MS, SCSG))-factorizability. In the second part of this article, we study the relationship between (R?,PSG)-factorizability and (MS,PSG)-factorizability.
Liang-Xue Peng, Ying Wang
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Every regular countably sieve-complete semitopological group is a topological group

Filomat
In this note, we firstly discuss some properties of spaces which are countably sieve-complete, densely q-complete and strongly Baire. By some known conclusions, we finally show that if G is a regular countably sieve-complete semitopological group then G is a topological group. If a regular semitopological group G has a dense subgroup which is countably
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On semitopological comopactifications of non-abelian groups

Semigroup Forum, 1980
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Complete ω-balancedness in semitopological groups

Topology and its Applications, 2018
A semitopological group is a group with a topology under which the operation is separately continuous. The authors characterize when such a group embeds into a product of strongly metrizable semitopological groups. The characterization reads: if and only if the group is completely \(\omega\)-balanced and satisfies \(Ir(G)\leq\omega\).
Juárez-Anguiano, Hugo, Sánchez, Iván
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Closure index of semitopological groups

Topology and its Applications, 2022
All spaces in this article satisfy the separation axiom \(T_1\). Let \(G\) be a group with a topology. The group \(G\) is called a semitopological group if multiplication in \(G\) is separately continuous and a paratopological group if multiplication is jointly continuous.
Martínez, Jonás, Tkachenko, Mikhail
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On ω s-balanced semitopological groups

Quaestiones Mathematicae, 2023
In this paper we introduce the notion of ωs-balanced semitopological groups. We show that a regular (Hausdorff, T1) semitopological group G admits a homeomorphic embedding as a subgroup into a product of regular (Hausdorff, T1) semitopological groups with a strong development if and only if G is ωs-balanced and Ir(G) ≤ ω (Hs(G) ≤ ω, Sm(G) ≤ ω).  ...
Kumar, Vikesh, Tyagi, Brij Kishore
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On reflections of quasitopological groups and semitopological groups

Topology and its Applications, 2022
A semitopological group \(G\) is a group endowed with a topology such that the multiplication operation on \(G\) is separately continuous. A paratopological group \(G\) is a group endowed with a topology such that the multiplication operation on \(G\) is jointly continuous. The \(T_{i}\)-reflection of a semitopological group \(G\) is a pair \((T_{i}(G),
Tang, Zhongbao, Chen, Mengna
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Projectively first-countable semitopological groups with certain D-properties

Topology and its Applications, 2022
In this paper, the authors give an internal characterization of subgroups of products of semitopological groups which satisfy certain properties that imply the \(D\)-property. For example, they give an internal characterization of subgroups of products of regular semitopological groups which satisfy open (G) and give an internal characterization of ...
Peng, Liang-Xue, Liu, Ying
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Productivity of Coreflective Subcategories of Semitopological Groups

Applied Categorical Structures, 2016
\textit{H. Herrlich} and \textit{M. Hušek} [Commentat. Math. Univ. Carol. 40, No. 3, 551--560 (1999; Zbl 1009.54041)] investigated productivity of coreflective subcategories \({\mathcal C}\) of topological groups. For example, they proved that a bicoreflective subcategory \(\mathcal C\) of \(\mathcal K\) is \(\kappa\)-productive provided it contains a \
Batíková, Bára, Hušek, Miroslav
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