Strongly topological gyrogroups with generalized countably compact properties

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2025-01-03 DOI:10.1016/j.topol.2024.109202

Jing Zhang, Kaixiong Lin

引用次数: 0

Abstract

In this note, some characterizations of strongly topological gyrogroups are given. It is proved that: (1) a strongly topological gyrogroup G has a q-point iff it is a quasi-perfect preimage of some metrizable space; (2) a strongly topological gyrogroup G has a strict q-point iff it is a sequential-perfect preimage of some metrizable space; (3) a strongly topological gyrogroup G contains a strong q-point iff it is a strongly sequential-perfect preimage of some metrizable space; (4) a strongly topological gyrocommutative gyrogroup G contains a pseudocompactness point iff there exists a continuous open mapping f from G onto a metrizable space M such that

f^{- 1} (F)

is an r-pseudocompact set in G for each r-pseudocompact set F in M.

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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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