关于伪有界和准拓扑群

Q3 Mathematics Matematychni Studii Pub Date : 2021-10-27 DOI:10.30970/ms.56.1.20-27
A. Ravsky, T. Banakh
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引用次数: 0

摘要

设$G$是一个准拓扑群。继F.~Lin和S.~Lin之后,我们证明了群$G$是伪有界的,如果对于$G$的单位元的任意邻域$U$,存在一个自然数$n$使得$U^n=G$。群$G$是$\ $-伪有界,如果对于$G$的单位元的任意邻域$U$,则群$G$是集合$U^n$的并集,其中$n$是自然数。群$G$是先验的,如果$G\ne N^ N$对于任何无处稠密的子集$G$和任何正整数$N$。本文研究了上述两类群之间的关系,并回答了F. Lin、S. Lin和S 'anchez提出的一些问题。
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On pseudobounded and premeage paratopological groups
Let $G$ be a paratopological group.Following F.~Lin and S.~Lin, we say that the group $G$ is pseudobounded,if for any neighborhood $U$ of the identity of $G$,there exists a natural number $n$ such that $U^n=G$.The group $G$ is $\omega$-pseudobounded,if for any neighborhood $U$ of the identity of $G$, the group $G$ is aunion of sets $U^n$, where $n$ is a natural number.The group $G$ is premeager, if $G\ne N^n$ for any nowhere dense subset $N$ of$G$ and any positive integer $n$.In this paper we investigate relations between the above classes of groups andanswer some questions posed by F. Lin, S. Lin, and S\'anchez.
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
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0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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