中文摘要：

可数sober空间是sober空间的一种推广．本文讨论了可数sober空间的一些性质，特别地证明了以可数sober空间为对象、以连续映射为态射的范畴CSOB为完备范畴以及从任意空间到可数sober空间的连续映射空间为可数sober空间．

英文摘要：

Countably sober spaces is a kind of generalization of sober spaces. In this paper, we discuss some properties of countably sober spaces. In particularly, we prove that the category CSOB with countably sober spaces and continuous mappings is a complete category, and the continuous mappings space from any space to a countably sober space is a countably sober space.