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《Journal of Mathematical Research and Exposition》 1982-01
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A Class of L-Fuzzy Topological Spaces Ⅰ. Neighborhood Structure of a L-Fuzzy Point

Li Zhongfu  
Suppose (L0,≤) is a poset (i.e. partially ordered set) with an order reversing involution and has an all element l. Let is a subset of L0 and satisfies the condition: if then is a complete and distributive lattice. L is called the lattice induced from poset L0. There is a mapping of a lattice L onto L. The mapping is clearly order reversing involution.Let X be a non-empty ordinary set. A function A from X to lattice L as called a L-fuzzy set in X. Xλ (where ) is called a L-fuzzy point. A L-fuzzy point Xλ is said to belong to a L-fuzzy set A, denoted by , iff . The complement of A denoted by A', is defined by the formula: .A L-fuzzy point Xλ is said to be quasi-coincident with A iff . We have the following theorem:Theorem (Dual principle). A L-fuzzy point Xλ is quasi-coincident with a L-fuzzy set A iff the L-fuzzy point A L-fuzzy set A is a Q-neighborhood of a L-fuzzy point xλ iff A is a neighborhood of the L-fuzzy pointIn this paper, all results of [2] (corresponding ones of [123 ch. I) have been generalized to the mentioned L-fuzzy topological spaces and some new theorems have been given;
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