{"title":"满足零维提升性质的有序紧的映射","authors":"B.D. Daniel , M. Tuncali , E.D. Tymchatyn","doi":"10.1016/j.topol.2025.109506","DOIUrl":null,"url":null,"abstract":"<div><div>Hoffmann has shown that each Peano continuum <em>X</em> is the continuous image of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> by a mapping satisfying the zero-dimensional lifting property (zdlp). He used this to give a wide range of characterizations of Peano continua. In this note, we begin to study the extension of Hoffman's result to the setting of continuous Hausdorff images of non-metric arcs. We give some necessary and some sufficient conditions for a compact Hausdorff space to be the continuous image of a linearly ordered compact space by a mapping satisfying the zdlp. It follows that each first countable dendron is the image of an ordered compactum under a map with zdlp. We also prove that each cyclic first countable image of an arc is the image of an ordered compactum under a mapping with zdlp.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"373 ","pages":"Article 109506"},"PeriodicalIF":0.5000,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mappings of ordered compacta satisfying the zero-dimensional lifting property\",\"authors\":\"B.D. Daniel , M. Tuncali , E.D. Tymchatyn\",\"doi\":\"10.1016/j.topol.2025.109506\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Hoffmann has shown that each Peano continuum <em>X</em> is the continuous image of <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> by a mapping satisfying the zero-dimensional lifting property (zdlp). He used this to give a wide range of characterizations of Peano continua. In this note, we begin to study the extension of Hoffman's result to the setting of continuous Hausdorff images of non-metric arcs. We give some necessary and some sufficient conditions for a compact Hausdorff space to be the continuous image of a linearly ordered compact space by a mapping satisfying the zdlp. It follows that each first countable dendron is the image of an ordered compactum under a map with zdlp. We also prove that each cyclic first countable image of an arc is the image of an ordered compactum under a mapping with zdlp.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"373 \",\"pages\":\"Article 109506\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2025-07-08\",\"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/S0166864125003049\",\"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/S0166864125003049","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Mappings of ordered compacta satisfying the zero-dimensional lifting property
Hoffmann has shown that each Peano continuum X is the continuous image of by a mapping satisfying the zero-dimensional lifting property (zdlp). He used this to give a wide range of characterizations of Peano continua. In this note, we begin to study the extension of Hoffman's result to the setting of continuous Hausdorff images of non-metric arcs. We give some necessary and some sufficient conditions for a compact Hausdorff space to be the continuous image of a linearly ordered compact space by a mapping satisfying the zdlp. It follows that each first countable dendron is the image of an ordered compactum under a map with zdlp. We also prove that each cyclic first countable image of an arc is the image of an ordered compactum under a mapping with zdlp.
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.