A note on unibasic spaces and transitive quasi-proximities
Submitted: 2015-08-27
|Accepted: 2017-03-02
|Published: 2017-04-03
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Keywords:
annular basis, entourage, semi-block, quasi-proximity, transitive quasi-proximity-uniformity, unibasic spaces
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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.
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