{"title":"Tychonoff Objects in the Topological Category of Cauchy Spaces","authors":"Muammer Kula, Sumeyye Kula","doi":"10.36753/MATHENOT.476787","DOIUrl":null,"url":null,"abstract":"There are various forms of Tychonoff objects for an arbitrary set-based topological category. In this paper, any explicit characterization of each of the Tychonoff Objects is given in the topological category of Cauchy spaces. Moreover, we characterize each of them for the category of Cauchy spaces and investigate the relationships among the various Ti, i = 0, 1, 2, 3, 4, PreT2, and T2 (we will refer to it as the usual one) structures are examined in this category.","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Sciences and Applications E-Notes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36753/MATHENOT.476787","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
There are various forms of Tychonoff objects for an arbitrary set-based topological category. In this paper, any explicit characterization of each of the Tychonoff Objects is given in the topological category of Cauchy spaces. Moreover, we characterize each of them for the category of Cauchy spaces and investigate the relationships among the various Ti, i = 0, 1, 2, 3, 4, PreT2, and T2 (we will refer to it as the usual one) structures are examined in this category.
对于任意基于集合的拓扑范畴，有各种形式的Tychonoff对象。本文给出了柯西空间拓扑范畴中每一个Tychonoff对象的任意显式刻划。此外，我们对它们中的每一个都进行了柯西空间范畴的表征，并研究了在这一类中检查的各种Ti, i = 0,1,2,3,4, PreT2和T2(我们将其称为通常的一个)结构之间的关系。
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