A note on unibasic spaces and transitive quasi-proximities

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

References

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H.-P. Künzi and M. J. Pérez-Peñalver, The number of compatible totally bounded quasi-uniformities, Act. Math. Hung. 88 (2000), 15-23. https://doi.org/10.1023/A:1006788124139

H.-P. Künzi and S. Watson, A nontrivial $T_1$-spaces admitting a unique quasi-proximity, Glasg. Math. J. 38 (1996), 207-213. https://doi.org/10.1017/S0017089500031451

W. J. Pervin. Quasi-uniformization of topological spaces, Math. Annalen 147 (1962), 116-117. https://doi.org/10.1007/BF01440953

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Published

2017-04-03

How to Cite

[1]
A. García-Máynez and A. Pimienta Acosta, “A note on unibasic spaces and transitive quasi-proximities”, Appl. Gen. Topol., vol. 18, no. 1, pp. 23–30, Apr. 2017.

Issue

Section

Regular Articles