Moore--Smith convergence in (L,M)-fuzzy topology

  • Authors:

  • Wei Yao

  • Affiliations:

  • Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang 050018, PR China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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Abstract

This paper presents a definition of (L,M)-fuzzy nets and the corresponding (L,M)-fuzzy generalized convergence spaces. It establishes a Moore-Smith convergence in (L,M)-fuzzy topology. It is shown that the category (L,M)-GConv of (L,M)-fuzzy generalized convergence spaces is topological, which embeds the category of (L,M)-fuzzy topological spaces as a reflective subcategory. It also defines a strong (L,M)-fuzzy generalized convergence space and shows that the resulting category S(L,M)-GConv is topological and Cartesian-closed, which also embeds the category of (L,M)-fuzzy topological spaces as a reflective subcategory and can be embedded in (L,M)-GConv as a coreflective subcategory. As a special case, (2,M)-GConv is cartesian-closed.