{"title":"New results regarding the lattice of uniform topologies on C(X)","authors":"Roberto Pichardo-Mendoza, Alejandro R'ios-Herrej'on","doi":"10.4995/agt.2023.18738","DOIUrl":null,"url":null,"abstract":"For a Tychonoff space X, the lattice UX was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology 39 (2021), 65-71.\nIn the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"25 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied general topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4995/agt.2023.18738","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For a Tychonoff space X, the lattice UX was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology 39 (2021), 65-71.
In the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X.
对于Tychonoff空间X，引入了格UX, L. a . psamrez - morales, G. Delgadillo-Piñón, R. Pichardo-Mendoza, C(X)上一致拓扑的格，一般拓扑问答39(2021)，65-71。在本文中，我们继续对用户体验进行研究。具体而言，本文在其前半部分涉及UX的结构和分类属性，而在其第二部分侧重于晶格的基本特征以及这些特征如何与空间X的一些基本函数相关。
期刊介绍：
The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.
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