The Hyperspaces C_n(X) of finite ray-graphs

2010/12/07 by Norah Esty, Esty, Norah
Mathematics · #54B20 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54B20

paper · pdf · doi:10.48550/arxiv.1012.1578

16 pages, 7 figures

arxiv created 2011/03/29 · arxiv updated 2011/03/30

Abstract

In this paper we consider the hyperspace C_n(X) of non-empty and closed subsets of a base space X with up to n connected components. We consider a class of base spaces called finite ray-graphs, which are a noncompact variation on finite graphs. We prove two results about the structure of these hyperspaces under different topologies (Hausdorff and Vietoris), in particular, about their number of connected components.

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