Connectedness of the Representation Space for Continua

Abstract

In on representation spaces, a forthcoming article, José G. Anaya, Félix Capulín, Włodzimierz J. Charatonik, and Fernando Orozco-Zitli have introduced the representation space C of all continua (up to homeomorphism). Here, we reproduce the argument that it is a topological space, and then we investigate its connectedness properties. Specifically, we show that C has exactly two components, and we demonstrate that the subspace N, consisting of all nondegenerate continua, is itself connected and even path connected. Moreover, we show that there exists a single continuum L such that N is the closure of the class of {L}. © 2011 Topology Proceedings.

Department(s)

Mathematics and Statistics

Keywords and Phrases

ε-mapping; (Metric) continua

International Standard Serial Number (ISSN)

0146-4124

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Auburn University; Nipissing University, All rights reserved.

Publication Date

31 Aug 2012

This document is currently not available here.

Share

 
COinS