Coset spaces with certain q-sequences

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-12-30 DOI:10.1016/j.topol.2024.109192

Jiewen Chen, Bin Zhao

{"title":"Coset spaces with certain q-sequences","authors":"Jiewen Chen, Bin Zhao","doi":"10.1016/j.topol.2024.109192","DOIUrl":null,"url":null,"abstract":"<div><div>Coset spaces with certain q-sequences are investigated. Firstly, we give some characterizations of strict q-spaces and strong q-spaces in coset spaces, and show that if H is a closed neutral subgroup of a topological group G, then <math><mi>G</mi><mo>/</mo><mi>H</mi></math> is a strict (resp., strong) q-space if and only if <math><mi>G</mi><mo>/</mo><mi>H</mi></math> is an open sequential-perfect (resp., strongly sequential-perfect) preimage of a metrizable space. Secondly, we discuss metrizability of coset spaces, and prove that if H is a closed neutral subgroup of a topological group G, then <math><mi>G</mi><mo>/</mo><mi>H</mi></math> is metrizable if and only if <math><mi>G</mi><mo>/</mo><mi>H</mi></math> is a sequential csf-countable q-space. Furthermore, if H is a compact subgroup of a topological group G, then <math><mi>G</mi><mo>/</mo><mi>H</mi></math> is metrizable if and only if <math><mi>G</mi><mo>/</mo><mi>H</mi></math> is a hereditarily normal strict q-space.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"361 ","pages":"Article 109192"},"PeriodicalIF":0.6000,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124003778","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

Coset spaces with certain q-sequences are investigated. Firstly, we give some characterizations of strict q-spaces and strong q-spaces in coset spaces, and show that if H is a closed neutral subgroup of a topological group G, then

G / H

is a strict (resp., strong) q-space if and only if

G / H

is an open sequential-perfect (resp., strongly sequential-perfect) preimage of a metrizable space. Secondly, we discuss metrizability of coset spaces, and prove that if H is a closed neutral subgroup of a topological group G, then

G / H

is metrizable if and only if

G / H

is a sequential csf-countable q-space. Furthermore, if H is a compact subgroup of a topological group G, then

G / H

is metrizable if and only if

G / H

is a hereditarily normal strict q-space.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

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.