On the relationship between limit spaces, many valued topological spaces, and many valued preorders

Authors:
Lingqiang Li;Dexue Zhang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu 610064, China;Department of Mathematics, Sichuan University, Chengdu 610064, China
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

Let (L,*,1) be a residuated complete lattice with the underlying lattice L a meet continuous lattice. This paper presents a systematic investigation of the interrelationship between the categories of limit spaces, L-topological spaces, and L-preorders. The results exhibit a close connection between these different mathematical structures.