The hyperspaces Cn(X) for finite ray-graphs

Norah Esty
DOI: https://doi.org/10.4995/agt.2013.1619

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).

Keywords

Hyperspaces; Finite graphs

Full Text:

PDF

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.

Abstract Views

1002
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share

 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Lifting Dynamical Properties to Hyperspaces
Dania Masood, Pooja Singh
Applied General Topology  vol: 15  issue: 2  first page: 175  year: 2014  
doi: 10.4995/agt.2014.1841



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt