A note on unibasic spaces and transitive quasi-proximities

Adalberto García-Máynez, Adolfo Pimienta Acosta

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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