CL(R) is simply connected under the Vietoris topology

CL(R) is simply connected under the Vietoris topology

In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales. We also present a construction of the (known) fact that this hyperspace is also p...

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Bibliographic Details
Main Author: N.C. Esty
Format: Article
Language:English
Published: Universitat Politècnica de València 2007-10-01
Series:Applied General Topology
Subjects:
Hyperspace
Vietoris topology
Simply connected
Path connected
Time scales
Online Access:http://polipapers.upv.es/index.php/AGT/article/view/1891
Description
Summary:In this paper we present a proof by construction that the hyperspace CL(R) of closed, nonemtpy subsets of R is simply connected under the Vietoris topology. This is useful in considering the convergence of time scales. We also present a construction of the (known) fact that this hyperspace is also path connected, as part of the proof.
ISSN:1576-9402
1989-4147

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