{"title":"Coincidence of the Dimensions of First Countable Spaces with a Countable Network","authors":"I.M. Leibo","doi":"10.1134/S1061920824030178","DOIUrl":null,"url":null,"abstract":"<p> The coincidence of the <span>\\( \\operatorname{Ind} \\)</span> and <span>\\(\\dim\\)</span> dimensions for the first countable paracompact <span>\\(\\sigma\\)</span>-spaces is proved. This gives a positive answer to A.V. Arkhangel’skii’s question of whether the dimensions <span>\\( \\operatorname{ind} X\\)</span>, <span>\\( \\operatorname{Ind} X\\)</span>, and <span>\\(\\dim X\\)</span> are equal for the first countable spaces with a countable network. </p><p> <b> DOI</b> 10.1134/S1061920824030178 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 3","pages":"568 - 570"},"PeriodicalIF":1.7000,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824030178","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The coincidence of the \( \operatorname{Ind} \) and \(\dim\) dimensions for the first countable paracompact \(\sigma\)-spaces is proved. This gives a positive answer to A.V. Arkhangel’skii’s question of whether the dimensions \( \operatorname{ind} X\), \( \operatorname{Ind} X\), and \(\dim X\) are equal for the first countable spaces with a countable network.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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