A note on unibasic spaces and transitive quasi-proximities

Adalberto García-Máynez, Adolfo Pimienta Acosta
DOI: https://doi.org/10.4995/agt.2017.4092

Abstract

In this paper we prove there is a bijection between the set of all annular bases of a topological spaces $(X,\tau)$ and the set of all transitive quasi-proximities on $X$ inducing $\tau$.

We establish some properties of those topological spaces $(X,\tau)$ which imply that $\tau$ is the only annular basis


Keywords

annular basis; entourage; semi-block; quasi-proximity, transitive quasi-proximity-uniformity; unibasic spaces.

Subject classification

Primary 54E05; 54E15; 54D35; Secondary 05C50.

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References

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1. Completion of pre-quasi-uniform spaces
Adalberto García-Máynez, Adolfo Pimienta Acosta
Topology and its Applications  vol: 221  first page: 491  year: 2017  
doi: 10.1016/j.topol.2017.02.025



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

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