Ideal-valued topological structures

  • Authors:

  • J. Gutiérrez García;T. Kubiak;A. P. Šostak

  • Affiliations:

  • Departamento de Matemáticas, Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain;Wydział Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, ul. Umultowska 87, 61-614 Poznań, Poland;Institute of Mathematics and CS, University of Latvia, LV-1586 Riga, Latvia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

With L a complete lattice and M a continuous lattice, this paper demonstrates an adjunction between M -valued L-topological spaces (i.e. (L,M )-topological spaces) and Idl(M )-valued L-topological spaces where Idl(M ) is the complete lattice of all ideals of M . It is shown that the right adjoint functor provides a procedure of generating (L,M )-topologies from antitone families of (L,M )-topologies. This procedure is then applied to give an internal characterization of joins in the complete lattice of all (L,M )-topologies on a given set.