Strongly Symmetric Compactifications

Keywords

Completely regular topological space; Limit tower space; Strong regularity; Strongly symmetric compactification

Abstract

Convergence approach spaces, defined by E. Lowen and R. Lowen [A quasitopos containing CONV and MET as full subcategories, Internat. J. Math. Math. Sci. 11 (1988)], possess both quantitative and topological properties. These spaces are equipped with a structure which provides information as to whether or not a sequence or filter approximately converges. Paul Brock and D. C. Kent [Approach spaces, limit tower spaces, and probabilistic convergence spaces, Appl. Categ. Structures 5 (1997)] show that the category of convergence approach spaces with contractions as morphisms is isomorphic to the category of limit tower spaces. Properties of the category of strongly symmetric limit tower spaces are studied here. In particular, a characterization of the limit tower spaces which possess a strongly symmetric compactification is given. Moreover, one-point strongly symmetric compactifications of limit tower spaces are studied.

Publication Date

1-1-2018

Publication Title

Topology Proceedings

Volume

52

Number of Pages

123-137

Document Type

Article

Personal Identifier

scopus

Socpus ID

85084211759 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85084211759

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