关于σ-空间的一个刻画

Characterize σ-space with CF-family and g-function

用CF 集族和g 函数来刻画了σ 空间 .即正则Frech啨ｔ空间Ｘ是σ 空间当且仅当在X上存在一个g 函数满足条件 (1) ,并且对每一个n∈N ,{g(n ,x)x∈X}是CF 集族 .条件 (1) :如果对每一个n∈N都有x∈g(n ,xn) ,则xn→x .

space is characterized in terms of CF family and g function.In the regular and Fréchet space, X is σ space if and only if X has a g function which satisfies condition (1)and for each n∈ N , {g(n,x)x∈X} is CF family. Condition (1): if for each n∈ N , x∈g(n,x n),then x n→ x .