不分明化拓扑线性空间（Ⅰ）

Fuzzifying Topological Linear Spaces(Ⅰ)

本文给出了不分明化拓扑线性空间的几个等价定义及其一些基本概念和性质，建立了原点邻城基对不分明线性拓扑的刻划性定理，得到了Ｈａｕｓｄｏｒｆｆ不分明化拓扑线性空间的等价性定理。

Several equal definitions of fuzzifying topological linear spaces are introduced and somemain properties are given. Especially we establish theorem which shows that for any linear spaceX, if ther exists satisfying six conditions, then there exists a fuzzifying linear topol ogy You X such that Bo is a neighbourhood base of o; conversely, if (X,ro is a fuzzifying topologi cal linear space, then there exists Boa at P(X) ) satisfying six conditions such that Bo is neighbour hood base of o. Finally we obtain theorem 2. 4 showing three equal proPOsitions in fuzzifyingtopological linear space.