拟邻域算子集合的基数

CARDINAL NUMBERS OF SET FOR PRE-NEIGHBOURHOOD OPERATORS

本文引出的0、Ⅰ、Ⅱ、Ⅲ型的拟邻域空间是拓扑空间不同程度的弱化与推广,在首先证明Ⅲ—型空间的闭包算子(?)具有性质 ①(?)=(?)(X)=X ②A(?)(A)③A(?)B(?)(A)(?)(B),及其逆命题的基础上给出了以下结果:|K_m(X)|=|D(X)|=|K_Ⅲ(X)/≌|=|D(X)/≌|=(?)。

The O.Ⅰ.Ⅱ.Ⅲ—type pre-neighbourhord spaces introdueed in this paperare the generalizations in different degrees of topological spaces.After wehave proved that the closure operator (?)ofⅢ—type space has properties①(?)(φ)=φ,(?)(X)=X.②A(?)(?)(A)③A(?)B(?)(?)(A)(?)(?)(B).and it′s converse theorem.we get the main results:|K_m(X)|=|D(X)|=|K_m(X)/≌|=|D(X)/≌|=2^(2|x|).