Hereditarily decomposable continua have non-block points

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-09-16 DOI:10.1016/j.topol.2024.109072

Daron Anderson

引用次数: 0

Abstract

In this note we expand upon our results from [1] to show that every nondegenerate hereditarily decomposable Hausdorff continuum has two or more non-block points, i.e. points whose complements contain a continuum-connected dense subset. The celebrated non-cut point existence theorem states that all nondegenerate Hausdorff continua have two or more non-cut points, and the corresponding result for non-block points is known to hold for metrizable continua. It is also known that there are consistent examples of Hausdorff continua with no non-block points, but that non-block point existence holds for Hausdorff continua that are either aposyndetic, irreducible, or separable.

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可遗传分解连续体具有非块点

在本注释中，我们扩展了[1]中的结果，证明每个非enerate 遗传可分解豪斯多夫连续体都有两个或两个以上的非块点，即其补集包含连续体连接密集子集的点。著名的非切点存在定理指出，所有非enerate Hausdorff 连续体都有两个或两个以上的非切点。人们还知道，有一些豪斯多夫连续体的一致例子不存在非块点，但非块点的存在对于无块、不可还原或可分离的豪斯多夫连续体是成立的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

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.

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