CL(R) is simply connected under the Vietoris topology

[EN] 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 a...

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Bibliographic Details
Author: Esty, N.C.
Format: article
Publication Date:2007
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/83073
Online Access:https://riunet.upv.es/handle/10251/83073
Access Level:Open access
Keyword:Hyperspace
Vietoris topology
Simply connected
Path connected
Time scales
Description
Summary:[EN] 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.