满足零维提升性质的有序紧的映射

IF 0.5 4区 数学 Q3 MATHEMATICS
B.D. Daniel , M. Tuncali , E.D. Tymchatyn
{"title":"满足零维提升性质的有序紧的映射","authors":"B.D. Daniel ,&nbsp;M. Tuncali ,&nbsp;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 ,&nbsp;M. Tuncali ,&nbsp;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}
引用次数: 0

摘要

Hoffmann通过满足零维提升性质(zdlp)的映射证明了每个Peano连续体X是[0,1]的连续像。他用这一点来给持续的皮亚诺一个广泛的特征。在这篇笔记中,我们开始研究将Hoffman的结果推广到非度量弧的连续Hausdorff像的设置。通过满足zdlp的映射,给出了紧化Hausdorff空间是线性有序紧化空间的连续像的充分必要条件。由此可见,每一个第一可数树突都是一个有序紧致在zdlp映射下的像。我们还证明了弧的每一个循环第一可数像都是一个有序紧实在与zdlp的映射下的像。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mappings of ordered compacta satisfying the zero-dimensional lifting property
Hoffmann has shown that each Peano continuum X is the continuous image of [0,1] 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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.20
自引率
33.30%
发文量
251
审稿时长
6 months
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信