A note on unibasic spaces and transitive quasi-proximities

• Autores: Adalberto García-Máynez, Adolfo Pimienta Acosta
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 1, 2017, págs. 23-30
• Idioma: inglés
• DOI: 10.4995/agt.2017.4092
• Enlaces
  • Texto completo
• Resumen

  • 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

• Referencias bibliográficas
  • P. Fletcher and W. Lindgren, Quasi-uniformity spaces, vol 77, Marcel Dekker, Inc., New York, First edition, 1982.
  • J. Ferrer, On topological spaces with a unique quasi-proximity, Quaest. Math 17 (1994), 479-486.
  • https://doi.org/10.1080/16073606.1994.9631779
  • H.-P. Künzi, Nontransitive quasi-uniformities in the Pervin quasi-proximity class, Proc. Amer. Math. Soc. 130 (2002), 3725-3730.
  • https://doi.org/10.1090/S0002-9939-02-06477-8
  • H.-P. Künzi, Quasi-uniform spaces-eleven years later, Topology Proceedings 18 (1993), 143-171.
  • H.-P. Künzi, Topological spaces with a unique compatible quasi-proximity, Arch. Math. 43 (1984), 559-561.
  • https://doi.org/10.1007/BF01190960
  • 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
  • W. J. Pervin, Quasi-proximities for topological spaces, Math. Annalen 150 (1963), 325-326.
  • https://doi.org/10.1007/BF01470761