On Representation Spaces

Author

• Jose G. Anaya
• Felix Capulin
• Enrique Castaneda-Alvarado
• W. J. Charatonik, Missouri University of Science and TechnologyFollow
• Fernando Orozco-Zitli

Abstract

Let C be a class of topological spaces, let P be a subset of C, and let α be a class of mappings having the composition property. Given X ∈ C, we write X ∈ Cl_α(P) if for every open cover U of X there is a space Y ∈ P and a U-mapping ƒ: X → Y that belongs to α. The closure operator Cl_α defines a topology τ_α in C. After proving general properties of the operator Cl_α, we investigate some properties of the topological space (ℕ, τ_α), where ℕ is the space of all nondegenerate metric continua and α is one of the following classes: all mappings, confluent mappings, or monotone mappings.

Recommended Citation

J. G. Anaya et al., "On Representation Spaces," Topology and its Applications, vol. 164, no. 1, pp. 1 - 13, Elsevier, Mar 2014.

The definitive version is available at https://doi.org/10.1016/j.topol.2013.08.012

Department(s)

Mathematics and Statistics

Keywords and Phrases

ε-Map; Arcwise connected; Chainability; Confluent mapping; Inverse limit; Local connected

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2014 Elsevier, All rights reserved.

Publication Date

01 Mar 2014