A note on arcs in hyperspaces
type: Item
instance of: scholarly article
title: A note on arcs in hyperspaces
zbMATH Open document ID: 0588.54013
DOI: 10.1007/BF01957022
author: B. George
published in: Acta Mathematica Hungarica
publication date: 1985-01-01T00:00:00Z
review text: Given a Hausdorff topological space X, the author considers the spaces \({\mathcal C}{\mathcal L}(X)\) of all nonempty closed subsets of X and \({\mathcal C}(X)\) of all connected compact subsets of X, both with the Vietoris topology. Then he proves a general arc theorem for the hyperspaces of X (i.e. the subspaces of \({\mathcal C}{\mathcal L}(X)\) which contain all singletons of X). From this theorem it follows that, if the space X is a continuum, then \({\mathcal C}{\mathcal L}(X)\) and \({\mathcal C}(X)\) are arcwise connected and locally arcwise connected.
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 3944801
zbMATH Keywords: arcwise connectedness
MaRDI profile type: Publication
cites work: Arcs, Semigroups, and Hyperspaces
cites work: Topologies on Spaces of Subsets
cites work: Q3869981
description: scientific article; zbMATH DE number 3944801