The hyperspaces Cn(X) for finite ray-graphs

Authors

  • Norah Esty Stonehill College

DOI:

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

Keywords:

Hyperspaces, Finite graphs

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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Author Biography

Norah Esty, Stonehill College

Department of Mathematics, Stonehill College, Easton, Massachusetts 02357

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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How to Cite

[1]
N. Esty, “The hyperspaces Cn(X) for finite ray-graphs”, Appl. Gen. Topol., vol. 14, no. 1, pp. 73–84, Apr. 2013.

Issue

Section

Regular Articles