Title

On Representation Spaces

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 XC, we write XClα(P) if for every open cover U of X there is a space YP and a U-mapping ƒ: XY that belongs to α. The closure operator Clα defines a topology τα in C. After proving general properties of the operator Clα, we investigate some properties of the topological space (ℕ, τα), 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.

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

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