具有CF性质的k-半分层空间

On k-semistratifiable Spaces with CF-property

给出了k-空间类中具有CF性质的k-半分层空间的一些刻画,证明了k-空间X是具有CF性质的k-半分层空间当且仅当X具有σ-CF闭伪基(闭k-网).作为这个结果的一个应用,本文部分正面回答了k-半分层空间的两个问题.

In this paper, we give some characterizations of k-semistratifiable spaces with CF-property, and prove that a k-space X is a k-semistratifiable space with CF-property if and only if it has a σ-CF closed pseudobase （closed k-network）. As an application of this result, we partially answer two questions On k-semistratifiable spaces with CF-property affirmatively.