Completion of pre-quasi-uniform spaces

The purpose in this paper is to prove the existence of a canonical-pre-quasi-uniform extension (X,U) ˆ of a pre-quasi-uniform space (X,U). Most of the concepts used in quasi-uniform spaces may be applied to pre-quasi-uniform spaces. These spaces were introduced by the first author and developed by t...

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Bibliographic Details
Published in:Topology and its applications 2017-04, Vol.221, p.491-500
Main Authors: García-Máynez, Adalberto, Pimienta Acosta, Adolfo
Format: Article
Language:English
Subjects:
[formula omitted]-Cauchy filter
Concrete
Connector
Filter
Minimal [formula omitted]-Cauchy filter
Mixing filters
Pre-quasi-uniformity
Pre-uniformity
Quasi-uniformity
Round filter
U-selective map
Uniformity
Unimorphism
Weakly round filters
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Summary:The purpose in this paper is to prove the existence of a canonical-pre-quasi-uniform extension (X,U) ˆ of a pre-quasi-uniform space (X,U). Most of the concepts used in quasi-uniform spaces may be applied to pre-quasi-uniform spaces. These spaces were introduced by the first author and developed by the second in his doctoral thesis. We shall study the main properties of this class of spaces which contains the class of quasi-uniform spaces.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.02.025