The hyperspaces Cn(X) for finite ray-graphs

Norah Esty

United States

Stonehill College

Department of Mathematics, Stonehill College, Easton, Massachusetts 02357

Submitted: 2013-07-26

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Accepted: 2013-07-26

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DOI: https://doi.org/10.4995/agt.2013.1619
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Keywords:

Hyperspaces, Finite graphs

Supporting agencies:

This research was not funded

Abstract:

In 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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References:

R. Duda, On the hyperspace of subcontinua of a finite graph I, Fund. Math. 62 (1968), 265–286.

R. Duda, On the hyperspace of subcontinua of a finite graph II, Fund. Math. 63 (1968), 225–255.

C. Eberhart and S. Nadler, Hyperspaces of cones and fans, Proc. Amer. Math. Soc. 77 (1979), no. 2, 279–288.

N. Esty, On the contractibility of certain hyperspaces, Top. Proc. 32 (2008), 291–300.

A. Illanes, The hyperspace C2(X) for a finte graph is unique, Glasnik Mat. 37 (2002), 347–363.

A. Illanes, Finite graphs X have unique hyperspaces Cn(X), Top. Proc. 27 (2003), 179–188.

A. Illanes and S. Nadler, Hyperspaces: Fundamentals and Recent Advances, Marcel Dekker, Inc., New York, 1999.

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