不分明嵌入理论及其应用

本文讨论一类格上拓扑学中嵌入问题,确切说是讨论值域为fuzzy格的L不分明拓扑空间中嵌入理论及其应用.首先概述若干诸如不分明单位区间、重域构造以及格上保并映射类的代数运算等基础性成果.其次给出不分明完全正则的点式刻划与关于一致结构的著名Weil定理的不分明推广并从而建立了在不分明单位方体中一般性的嵌入定理.最后作为嵌入定理的应用,得到了不分明Urysohn度量化定理并完成了不分明Stone-Cech紧化的一般理论。

Fuzzy Imbedding Theory and Its Applications

This paper deals with the imbedding problem in the lattices with a topology. Precisely, we discuss the imbedding problem in L-fuzzy topological space, where L is a fuzzy lattice. Some fundamental results such as the fuzzy unit intezval, Q-nei-ghborhood structure and algebraic properties of union-preserving maps in lattices are collected. A pointwise characterization of fuzzy complete regularity is yielded by means of the Q- neighborhood structures and some algebraic properties of certain class of maps in lattices. The Weil theorem on fuzzy uniformity and the general imbedding theorem in the fuzzy basic cube are established. As applications of the imbedding theorem, a fuzzy version of the well-known Urysohn metrizable theorem and the general theory of the fuzzy Stone-Cech compactification are given.