{"title":"On Tightness-Type Properties of the Space of Weakly Additive Functionals","authors":"Sh. A. Ayupov, N. K. Mamadaliev","doi":"10.1134/s0081543824010036","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study tightness-type properties such as tightness, minitightness, and local density of the space of weakly additive functionals with finite support. We also investigate some generalizations of continuous functions. Furthermore, we present an extension of the functor of weakly additive functionals with finite support to the class of strictly <span>\\(\\tau\\)</span>-continuous mappings. We introduce two extensions of the categories <span>\\(\\mathrm{Comp}\\)</span> and <span>\\(\\mathrm{Tych}\\)</span> (of compact and Tychonoff spaces, respectively). One of the main results of the paper is that the functor <span>\\(O_n\\)</span> of weakly additive functionals with finite support preserves the tightness character of infinite compact spaces. In addition, we show that the local densities of the spaces <span>\\(X\\)</span> and <span>\\(O_n(X)\\)</span> coincide for any infinite compact space <span>\\(X\\)</span>. </p>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Steklov Institute of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543824010036","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study tightness-type properties such as tightness, minitightness, and local density of the space of weakly additive functionals with finite support. We also investigate some generalizations of continuous functions. Furthermore, we present an extension of the functor of weakly additive functionals with finite support to the class of strictly \(\tau\)-continuous mappings. We introduce two extensions of the categories \(\mathrm{Comp}\) and \(\mathrm{Tych}\) (of compact and Tychonoff spaces, respectively). One of the main results of the paper is that the functor \(O_n\) of weakly additive functionals with finite support preserves the tightness character of infinite compact spaces. In addition, we show that the local densities of the spaces \(X\) and \(O_n(X)\) coincide for any infinite compact space \(X\).
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
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