Results 11 to 20 of about 271 (88)

Suitable sets for paratopological groups [PDF]

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021
A paratopological group $G$ has a {\it suitable set} $S$. The latter means that $S$ is a discrete subspace of $G$, $S\cup \{e\}$ is closed, and the subgroup $\langle S\rangle$ of $G$ generated by $S$ is dense in $G$. Suitable sets in topological groups were studied by many authors.
Lin, Fucai, Ravsky, Alex, Shi, Tingting
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★-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
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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
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Lindelöf Σ-Spaces and R-Factorizable Paratopological Groups

Axioms, 2015
We prove that if a paratopological group G is a continuous image of an arbitrary product of regular Lindelöf Σ -spaces, then it is R-factorizable and has countable cellularity.
Mikhail Tkachenko
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A note on compact-like semitopological groups

Karpatsʹkì Matematičnì Publìkacìï, 2019
We present a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is provided a semiregular semitopological group $G$ which is not $T_3$.
A. Ravsky
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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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