The hyperspaces Cn(X) for finite ray-graphs
Keywords:Hyperspaces, Finite graphs
AbstractIn this paper we consider the hyperspace Cn(X) of non-empty and closed subsets of a base space X with up to n connected components. The class of base spaces we consider we call finite ray-graphs, and are a noncompact variation on finite graphs. We prove two results about the structure of these hyperspaces under different topologies (Hausdorff metric topology and Vietoris topology).
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