图的非切次连续的超空间

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-07-31 DOI:10.1016/j.topol.2025.109533

Alejandro Illanes , Verónica Martínez-de-la-Vega , Jorge E. Vega

引用次数: 0

摘要

给定连续体X，设C(X)是X的所有子连续体的超空间。我们考虑超空间NC (X)={a∈C(X):X∈a是连通的}。在本文中，我们证明了NC _ (X)紧致的局部连通连续体X只有圆弧和简单闭合曲线。我们还刻画了NC (G)连通的有限图G。

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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The hyperspace of non-cut subcontinua of graphs

Given a continuum X, let

C (X)

be the hyperspace of all subcontinua of X. We consider the hyperspace

N C^{⁎} (X) = {A \in C (X) : X ∖ A

is connected}. In this paper we prove that the only locally connected continua X for which

N C^{⁎} (X)

is compact are the arcs and the simple closed curves. We also characterize the finite graphs G for which

N C^{⁎} (G)

is connected.

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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.