{"title":"强超对称保值函数","authors":"Oleksiy Dovgoshey","doi":"10.1016/j.topol.2024.108931","DOIUrl":null,"url":null,"abstract":"<div><p>An ultrametric preserving function <em>f</em> is said to be strongly ultrametric preserving if ultrametrics <em>d</em> and <span><math><mi>f</mi><mo>∘</mo><mi>d</mi></math></span> define the same topology on <em>X</em> for each ultrametric space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span>. The set of all strongly ultrametric preserving functions is characterized by several distinctive features. In particular, it is shown that an ultrametric preserving <em>f</em> belongs to this set iff <em>f</em> preserves the property to be compact.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Strongly ultrametric preserving functions\",\"authors\":\"Oleksiy Dovgoshey\",\"doi\":\"10.1016/j.topol.2024.108931\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>An ultrametric preserving function <em>f</em> is said to be strongly ultrametric preserving if ultrametrics <em>d</em> and <span><math><mi>f</mi><mo>∘</mo><mi>d</mi></math></span> define the same topology on <em>X</em> for each ultrametric space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></span>. The set of all strongly ultrametric preserving functions is characterized by several distinctive features. In particular, it is shown that an ultrametric preserving <em>f</em> belongs to this set iff <em>f</em> preserves the property to be compact.</p></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-25\",\"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/S0166864124001160\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124001160","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
摘要
如果超度量 d 和 f∘d 为每个超度量空间 (X,d) 定义了 X 上的相同拓扑，则称超度量保全函数 f 为强超度量保全函数。所有强超对称保留函数的集合有几个显著特点。特别是，如果 f 保留了紧凑的性质，那么超对称保留 f 就属于这个集合。
An ultrametric preserving function f is said to be strongly ultrametric preserving if ultrametrics d and define the same topology on X for each ultrametric space . The set of all strongly ultrametric preserving functions is characterized by several distinctive features. In particular, it is shown that an ultrametric preserving f belongs to this set iff f preserves the property to be compact.
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.
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