关于连续函数格C（X，R￣＊）的一个注记

NOTES ON THE LATTICE OF CONTINUOUS FUNCTIONS

证明了如下结果：若拓扑空间Ｘ的开集格Ω（Ｘ）满足Ｖ－无穷分配律，则连续函数格Ｃ（Ｘ。

It is known that the lattice of continuous extended-real-valued functions C(X,R),in general,is not complete。 In this note, we show that for a topological space X,c(X,R )is a completeHeyting algebra (cHa)if its open sets lattice satisfies V-infinite distributive law in terms of Frame morphism。 As a consequence,we obtain the result that C(X,R ) is a cHa if X is strong connected space。