完全不连通集合的超空间

Pub Date : 2020-06-12 DOI:10.3336/gm.55.1.10

R. Escobedo, P. Pellicer-Covarrubias, V. Sánchez-Gutiérrez

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引用次数: 0

摘要

本文研究了具有Vietoris拓扑的空间中所有非空闭完全不连通子集的超空间。我们给出了这个超空间的紧性、连通性和局部连通性的结果。我们还研究了路径连通性，特别是证明了对于光滑树状体，该超空间是路径连通的，并给出了一个一般结果，该结果表明对于欧几里德空间，该超空间具有不可数的弧分量。

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 totally disconnected sets

In this paper we study the hyperspace of all nonempty closed totally disconnected subsets of a space, equipped with the Vietoris topology. We show results of compactness, connectedness and local connectedness for this hyperspace. We also include a study of path connectedness, particularly we prove that for a smooth dendroid this hyperspace is pathwise connected, and we present a general result which implies that for an Euclidean space this hyperspace has uncountably many arc components.

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