A note on unibasic spaces and transitive quasi-proximities

Author:

García-Máynez Adalberto,Pimienta Acosta Adolfo

Abstract

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

Publisher

Universitat Politecnica de Valencia

Subject

Geometry and Topology

Reference8 articles.

1. P. Fletcher and W. Lindgren, Quasi-uniformity spaces, vol 77, Marcel Dekker, Inc., New York, First edition, 1982. https://doi.org/10.1080/16073606.1994.9631779 https://doi.org/10.1090/S0002-9939-02-06477-8

2. ON TOPOLOGICAL SPACES WITH A UNIQUE QUASI-PROXIMITY

3. Nontransitive quasi-uniformities in the Pervin quasi-proximity class

4. Topological spaces with a unique compatible quasi-proximity

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