L-Fuzzy连续函数格

The Lattices of L-Fuzzy Continuous Functions

本文讨论了L-Fuzzy拓扑空间到L-Fuzzy实直线R(L)的所有L-Fuzzy连续函数的格C(L^x)的代数性质与(L^x,δ)的拓扑性质——紧性的关系;指出了L^x上的L-Fuzzy拓扑可以用格C(L^x)直接刻划。并且构造了L-Fuzzy Stone拓扑;通过代数方法较简单地证明了Tychonoff乘积定理。

In this paper, we discuss the relation between the algebraic properties of the lattice C(L^x) which is all L-fuzzy continuous functions from a L-fuzzy topological space (L^x,δ) to L-fuzzy real-valued line R(L) and topological compactness. We also show that the L-fuzzy topology on the L^x can be described by the lattice C(L^x), and construct L-fuzzy Stone topology. We prove easily Tychonoff product theorem by algebraic method.