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On ω s-balanced semitopological groups
Quaestiones Mathematicae, 2023In 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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Closure index of semitopological groups
Topology and its Applications, 2022All 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 reflections of quasitopological groups and semitopological groups
Topology and its Applications, 2022A 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, 2022In 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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Two questions on coset spaces of semitopological groups
Topology and its Applications, 2023Let \(G\) be a semitopological group. The family of all open neighborhoods of the identity \(e\) is denoted by \(\mathcal{N}_{G}(e)\). A subgroup \(H\) of \(G\) is called \textit{neutral} if for every \(U\in\mathcal{N}_{G}(e)\), there exists a \(V\in\mathcal{N}_{G}(e)\) such that \(HV\subseteq UH\) and \(VH\subseteq HU\).
Li, Piyu +3 more
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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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Subgroups of products of metrizable semitopological groups
Monatshefte für Mathematik, 2016In [Topology Appl. 156, No. 7, 1298--1305 (2009; Zbl 1166.54016)], \textit{M. Tkachenko} posed the problem to characterize the projectively metrizable paratopological groups, i.e., the subgroups of topological products of metrizable paratopological groups. The present paper gives an answer to the above problem.
I. Sánchez
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Projectively regular (T2, T1) weakly developable semitopological groups
Topology and its ApplicationsThe authors introduce the notion of weakly \(\omega\)-balanced semitopological groups and prove that the class of weakly \(\omega\)-balanced semitopological groups is closed under taking subgroups and products. The authors also show that a regular (Hausdorff, \(T_1\)) semitopological group \(G\) admits a homeomorphic embedding as a subgroup into a ...
Vikesh Kumar, Brij Kishore Tyagi
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Continuity of operations in right semitopological groups
Topology and its ApplicationsThis paper is an attempt at a systematization of the multiple ways in which a topology can interact with a group structure, starting with the minimum requirement that the resulting object is at least a right semitopological semigroup. The author considers mainly conditions based on weakened forms of continuity of the operations, semi-neighborhoods of ...
E. Reznichenko
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Semitopological groups, semiclosure semigroups and quantales
Fuzzy Sets and Systems, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Shengwei, Xia, Changchun, Zhao, Bin
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