{"title":"Non-cut ordered arcs of the hyperspace of subcontinua","authors":"José G. Anaya, David Maya","doi":"10.1016/j.topol.2024.108908","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> be the hyperspace of all subcontinua of a continuum <em>X</em> topologized by Hausdorff metric. For a non-empty closed subset <em>A</em> of a continuum <em>X</em>, consider the following properties: <em>A</em> is a strong non-cut subset, non-block subset, weak non-block subset, shore subset, not a strong center, and non-cut subset of <em>X</em>. The aim of this paper is to study the conditions under which an ordered arc from a singleton to a proper subcontinuum of a continuum <em>X</em> has one of these properties in <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-10","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/S0166864124000932","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
Abstract
Let be the hyperspace of all subcontinua of a continuum X topologized by Hausdorff metric. For a non-empty closed subset A of a continuum X, consider the following properties: A is a strong non-cut subset, non-block subset, weak non-block subset, shore subset, not a strong center, and non-cut subset of X. The aim of this paper is to study the conditions under which an ordered arc from a singleton to a proper subcontinuum of a continuum X has one of these properties in .
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.