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
• Enlaces
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• 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.