Some properties of pre-topological groups

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-01-08 DOI:10.1016/j.topol.2025.109204

Fucai Lin , Ting Wu , Yufan Xie , Meng Bao

引用次数: 0

Abstract

In this paper, the concepts of pre-topological groups and some generalizations of pre-topological groups are posed. First, some basic properties of pre-topological groups are systematically investigated; in particular, we prove that each

T_{0}

pre-topological group is regular, and every

T_{0}

almost topological group is completely regular which extends A.A. Markov's theorem to the class of almost topological groups. Moreover, it is shown that an almost topological group is τ-narrow if and only if it can be embedded as a subgroup of a pre-topological C-product of almost topological groups of weight less than or equal to τ. Finally, the cardinal invariant, the precompactness and the resolvability are investigated in the class of pre-topological groups.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.

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