函数空间Cp(X)与有限乘积空间的弱Lindelof性

Function space Cp(X) and weak Lindelf properties of finite powers of a space X

给出了空间 Ｘ 与 Ｘ 的有限乘积空间的两种弱 Ｌｉｎｄｅｌｏｆ 对偶性并证明了当 Ｘ是 Ｐ 空间时，对于 每个 ｎ ∈ ω， Ｘｎ 为拟 Ｌｉｎｄｅｌｏｆ空间当且仅当ｔ（ Ｃｐ （ Ｘ）） ＝

In this paper, it is shown that: (1) for every n∈ω, X n is *Lindelf space if and only if X satisfies condition (ε′), (2) for every n∈ω, X n is quasi Lindelf space if and only if X satisfies condition (ε″), (3) if X is P space, X n is quasi Lindelf space if and only if t(Cp(X))=ω. 