石墨和枝晶非切割亚连续的超空间

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2021-08-13 DOI:10.4064/cm8947-9-2022

Rodrigo Hern'andez-Guti'errez, Ver'onica Mart'inez-de-la-Vega, Jorge M. Mart'inez-Montejano, Jorge E. Vega

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引用次数: 0

摘要

给定一个连续体$X$，设$C（X）$表示$X$的所有子连续体的超空间。本文研究了当$X$是有限图或枝晶时，C（X）中的Vietoris超空间$NC^{*}（X）=\｛A\：X\setminus A\text｛是连通的｝\｝$；特别地，我们给出了$NC^{*}（X）$是紧致的、连通的、局部连通的或完全不连通的条件。此外，我们还证明了如果$X$是枝晶，并且$X$的端点集是稠密的，那么$NC^{*}（X）$同胚于无理数的Baire空间。

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The hyperspace of noncut subcontinua of graphs and dendrites

Given a continuum $X$, let $C(X)$ denote the hyperspace of all subcontinua of $X$. In this paper we study the Vietoris hyperspace $NC^{*}(X)=\{ A \in C(X):X\setminus A\text{ is connected}\}$ when $X$ is a finite graph or a dendrite; in particular, we give conditions under which $NC^{*}(X)$ is compact, connected, locally connected or totally disconnected. Also, we prove that if $X$ is a dendrite and the set of endpoints of $X$ is dense, then $NC^{*}(X)$ is homeomorphic to the Baire space of irrational numbers.

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.