On Representation Spaces
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 ∈ Clα(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 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.
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
Mathematics and Statistics
Keywords and Phrases
ε-Map; Arcwise connected; Chainability; Confluent mapping; Inverse limit; Local connected
International Standard Serial Number (ISSN)
Article - Journal
© 2014 Elsevier, All rights reserved.
01 Mar 2014