Results 11 to 20 of about 346 (87)

★-quasi-pseudometrics on algebraic structures

Applied General Topology, 2023
In this paper, we introduce some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space.
Shi-Yao He, Ying-Ying Jin, Li-Hong Xie
doaj   +1 more source

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Axioms, 2021
This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids).
Mikhail G. Tkachenko
doaj   +1 more source

Remainders of Semitopological Groups or Paratopological Groups [PDF]

Ukrainian Mathematical Journal, 2014
All spaces are assumed to be Tychonoff. The authors prove results about remainders of Hausdorff compactifications of paratopological or semitopological groups. The following results are typical: If a nonlocally compact semitopological group \(G\) has a Hausdorff compactification \(bG\) such that the remainder \(bG{\setminus} G\) is locally metrizable ...
Lin, Fucai, Liu, Chuan, Xie, Li-Hong
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Almost paratopological groups

Topology and its Applications, 2023
A class of almost paratopological groups is introduced, which (1) contains paratopological groups and Hausdorff quasitopological groups; (2) is closed under products; (3) subgroups. Almost paratopological $T_1$ groups $G$ are characterized by the fact that $\{(x,y)\in G^2: xy=e\}$ is closed in $G^2$.
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Characterizing s-paratopological groups by free paratopological groups

Topology and its Applications, 2017
In [Trans. Am. Math. Soc. 149, 187--198 (1970; Zbl 0229.54028)], \textit{N. Noble} defined an important class of topological groups, namely, the class of \(s\)-groups. A Hausdorff topological group \(G\) is called an \textit{\(s\)-group} if every sequentially continuous homomorphism \(p\) from \(G\) to a topological group \(H\) is continuous (recall ...
Cai, Zhangyong, Lin, Shou, Tang, Zhongbao   +2 more
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Weak completions of paratopological groups [PDF]

Topology and its Applications, 2021
Given a $T_0$ paratopological group $G$ and a class $\mathcal C$ of continuous homomorphisms of paratopological groups, we define the $\mathcal C$-$semicompletion$ $\mathcal C[G)$ and $\mathcal C$-$completion$ $\mathcal C[G]$ of the group $G$ that contain $G$ as a dense subgroup, satisfy the $T_0$-separation axiom and have certain universality ...
Banakh, Taras, Tkachenko, Mikhail
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Subgroups of paratopological groups and feebly compact groups

Applied General Topology, 2014
It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup.
Manuel Fernández, Mikhail G. Tkachenko
doaj   +1 more source

Partially paratopological groups

Topology and its Applications, 2017
The paper uses the notion of partially topological space which is a slight modification of the notion of generalized topological space of Delfs and Knebusch. Intuitively, a partially topological space is a set \(X\) with a system \(\text{Cov}_X\) of ``admissible'' families of open sets where a union of open sets is open only if it is the union of an ...
Al Shumrani, Mohammed, Piekosz, Artur, Wajch, Eliza, Ozel, Cenap   +3 more
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Feebly compact paratopological groups and real-valued functions [PDF]

, 2012
We present several examples of feebly compact Hausdorff paratopological groups (i.e., groups with continuous multiplication) which provide answers to a number of questions posed in the literature.
Sanchis López, Manuel, Tkachenko, Mikhail   +1 more
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Notes on Remainders of Paratopological Groups [PDF]

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2014
The remainder of a Tychonoff topological space \(X\) is the subspace \(bX\setminus X\) of some compactification \(bX\) of \(X\). The authors study remainders of paratopological and of semitopological groups \(G\), in particular they relate properties of \(G\) with properties of the remainder \(bG\setminus G\).
Wang, Hanfeng, He, Wei
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