Introduction to generalized topological spaces

• Zvina, Irina ^[1]
  1. [1] University of Latvia

     University of Latvia

     Letonia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 12, Nº. 1, 2011, págs. 49-66
• Idioma: inglés
• DOI: 10.4995/agt.2011.1701
• Enlaces
  • Texto completo
• Resumen

  • We introduce the notion of generalized topological space (gt-space). Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants) in terms of generalized spaces.

• Referencias bibliográficas
  • L. M. Brown and M. Diker, Ditopological texture spaces and intuitionistic sets, Fuzzy Sets Syst. 98, no. 2 (1998), 217–224 http://dx.doi.org/10.1016/S0165-0114(97)00358-8
  • S. Givant and P. Halmos, Introduction to Boolean Algebras, Springer Science+Business Media, LLC (2009)
  • T. R. Hamlett and D. Jankovic, Ideals in topological spaces and the set operator , Boll. Unione Mat. Ital., VII. Ser., B 4, no. 4 (1990),...
  • T. R. Hamlett and D. Jankovic, Ideals in general topology, General topology and applications, Proc. Northeast Conf., Middletown, CT (USA),...
  • D. Jankovic and T. R. Hamlett, New topologies from old via ideals, Am. Math. Mon. 97, no.4 (1990), 295–310. http://dx.doi.org/10.2307/2324512
  • D. Jankovic and T. R. Hamlett, Compatible extensions of ideals, Boll. Unione Mat. Ital., VII. Ser., B 6, no.3 (1992), 453–465.
  • D. Jankovic, T. R. Hamlett and Ch. Konstadilaki, Local-to-global topological properties, Math. Jap. 52, no.1 (2000), 79–81.
  • I. Zvina, Complete infinitely distributive lattices as topologies modulo an ideal, Acta Univ. Latviensis, ser. Mathematics, 688 (2005), 121–128
  • I. Zvina, On i-topological spaces: generalization of the concept of a topological space via ideals, Appl. Gen. Topol. 7, no. 1 (2006), 51–66