Lattice-valued induced fuzzy topological spaces

  • Authors:
  • Yueli Yue

  • Affiliations:
  • Department of Mathematics, Ocean University of China, Qingdao, 266071, PR China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

The aim of this paper is to study induced LM-fuzzy topological spaces. Firstly, we study the stratifications of LM-fuzzy topologies and show that SLM-FTOP-the category of stratified LM-fuzzy topological spaces-is a coreflective full subcategory of LM-FTOP. Secondly, we study Kubiak-Lowen functors @w and @i in LM-fuzzy topological spaces. We prove that M-FYS is isomorphic to ILM-FTOP-the category of induced LM-fuzzy topological spaces-and ILM-FTOP is a reflective and coreflective full subcategory of SLM-FTOP. Finally, we study weakly induced modification of LM-fuzzy topologies and show that WILM-FTOP-the category of weakly induced LM-fuzzy topological spaces-is a reflective and coreflective full subcategory of LM-FTOP.