Results 71 to 80 of about 590 (104)

Two questions on coset spaces of semitopological groups

Topology and its Applications, 2023
Let \(G\) 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, Mou, Lei, Shen, Rongxin, Xu, Yanqin   +3 more
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Semitopological groups, semiclosure semigroups and quantales

Fuzzy Sets and Systems, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Shengwei, Xia, Changchun, Zhao, Bin
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Right Topological and Semitopological Groups

2008
It frequently happens in Mathematics that the study of certain rich structures (like Hilbert or Banach spaces, or bounded linear operators acting on these spaces) requires a detailed knowledge of some weaker structures (locally convex linear topological spaces or, respectively, topological semigroups).
Alexander Arhangel’skii, Mikhail Tkachenko   +1 more
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THE BAIRE PROPERTY IN THE REMAINDERS OF SEMITOPOLOGICAL GROUPS

Bulletin of the Australian Mathematical Society, 2013
AbstractIt is proved that every remainder of a nonlocally compact semitopological group $G$ is a Baire space if and only if $G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279],
Xie, Li-Hong, Lin, Shou
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Projectively regular (T2, T1) weakly developable semitopological groups

Topology and its Applications
The 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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Subgroups of products of certain paratopological (semitopological) groups

Topology and its Applications, 2018
The authors investigate some properties of subgroups of products of certain paratopological (semitopological) groups. The following main results are proved: (1)\, Let \(G\) be an \(\omega\)-balanced regular paratopological group with \(Ir(G)\leq \omega\). Let \(e\) be the identity of \(G\). If for each \(U \in \mathscr{N}(e)\) there exist some \(V \in \
Peng, Liang-Xue, Guo, Ming-Yue
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Some three-space properties of semitopological and paratopological groups

Topology and its Applications, 2019
All spaces are assumed to be Hausdorff. Recall that a \textit{semitopological group} is a group with a topology such that the multiplication in the group is separately continuous, a \textit{quasitopological group} is a semitopological group with the additional property that the inverse mapping is continuous and a \textit{paratopological group} is a ...
Li, Piyu, Mou, Lei, Wang, Hanfeng, Xie, Li-Hong   +3 more
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On locally p⁎⁎-spaces and remainders of semitopological groups

Topology and its Applications, 2019
Abstract We study the compactification of semitopological groups with remainders being locally p ⁎ ⁎ -spaces, and establish: (1) if a semitopological group X has a remainder that is locally a p ⁎ ⁎ -space, then either X is a paracompact p-topological group, or X is meager; (2) if a non-locally compact paratopological group X
Hanfeng Wang, Wei He, Jing Zhang
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Subgroups of products of metrizable semitopological groups

Monatshefte für Mathematik, 2016
In [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.
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Paratopological and Semitopological Groups Versus Topological Groups

2013
We present a survey on paratopological and semitopological groups relating these classes with the class of topological groups. A special attention is given to compactness-type properties in paratopological and semitopological groups which often imply automatic continuity of inversion or multiplication (or both) in these classes of objects.
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