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 f:X→Y that belongs to α. The closure operator Clα defines a topology τα i...

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Bibliographic Details
Published in:Topology and its applications 2014-03, Vol.164, p.1-13
Main Authors: Anaya, José G., Capulín, Félix, Castañeda-Alvarado, Enrique, Charatonik, Włodzimierz J., Orozco-Zitli, Fernando
Format: Article
Language:English
Subjects:
Arcwise connected
Chainability
Confluent mapping
Inverse limit
Local connected
ε-Map
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Summary: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 f: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.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2013.08.012