摘要
在最广泛的完备格框架下引入了一种新的代数结构,即三角结构,它是L上满足适当条件的一种关系。在一定条件下L上的三角结构与L上的自映射可以互相转化。基于这一事实,内部算子、闭包算子、近性结构(proximity)以及近年来在完全分配格上建立的拟一致结构理论和Katsaras在Fuzzy集框架下提出的泛拓扑结构(Syntopogenous Structure)理论等都可以统一于三角结构理论之中。
A new algebraic structure, Δ-structure, is introduced under a fairly wide frame on complete lattices. It is a certain relation on L_The Δ-structures on L can be transformed into certain self-mappings on L under proper conditions, and therefrom it can be proved that all the theories of interio, operator, closure operator, proximities, quasi-uniformi ties on completely distributive lattices which have developed rapidly in recent years, and the theory of syntopogenous structure proposed by Katsaras under the frame of fuzzy sets can be unified within the theory of Δ-structures.
出处
《陕西师大学报（自然科学版）》
CSCD
1990年第2期1-15,共15页
Journal of Shaanxi Normal University(Natural Science Edition)
基金
国家自然科学基金
关键词
完备格
三角结构
拟一致结构
complete lattice
upper(lower) triangle
upper (lower)Δ-structure
upper (lower) quasi-uniformity
proximily
