Approximations by disjoint subcontinua and indecomposability

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-09-27 DOI:10.1016/j.topol.2024.109071

David S. Lipham

引用次数: 0

Abstract

We study approximations of continuum-wise connected spaces, or semicontinua, and show that every indecomposable semicontinuum can be approximated from within by a sequence of pairwise disjoint continua. As a corollary, we find that if X is a G-like continuum or a one-dimensional non-separating plane continuum, which is the closure of an indecomposable semicontinuum, then X is indecomposable. We also prove that a composant of an indecomposable continuum cannot be embedded into a Suslinian continuum.

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不相邻子连续体的逼近和不可分解性

我们研究了连续面连接空间或半连续面的近似，并证明每个不可分解的半连续面都可以从内部被一连串成对相离的连续面近似。作为推论，我们发现如果 X 是类 G 连续体或一维非分离平面连续体（即不可分解半连续体的闭包），那么 X 是不可分解的。我们还证明了不可分解连续统的合成子不能嵌入到苏斯林连续统中。

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.