A note on unibasic spaces and transitive quasi-proximities

Adalberto García-Máynez; Adolfo Pimienta Acosta

doi:10.4995/agt.2017.4092

Authors

Adalberto García-Máynez Universidad Nacional Autónoma de México
Adolfo Pimienta Acosta Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.4995/agt.2017.4092

Keywords:

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

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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Author Biographies

Adalberto García-Máynez, Universidad Nacional Autónoma de México

Instituto de Matemáticas

Area de la Investigación Científica Circuito Exterior

Adolfo Pimienta Acosta, Universidad Autónoma Metropolitana

Departamento de Matemáticas

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