可数S-闭空间及可数仿S-闭空间

THE COUNTABLE S-CLOSED SPACES AND COUNTABLE PARA-S-CLOSED SPACES

文章引进了可数Ｓ－闭空间和可数仿Ｓ－闭空间的概念，并研究了它们的一些性质，在Ｐ_∑~＊型空间中讨论了它们与极不连通空间、可数紧空间、可数仿紧空间的关系，得出：在极不连通空间中．可数紧一定可数Ｓ－闭、可数仿紧一定可数仿Ｓ－闭；Ｐ_∑~＊空间中、可数Ｓ－闭一定可数紧．极不连通、可数仿Ｓ－闭一定可数仿Ｓ－闭，极不连通；空间（Ｘ．）是可数Ｓ－闭空间（可数仿Ｓ－闭空间）．当且仅当它的半正则化（Ｘ．）是可数Ｓ－闭空间（可数仿Ｓ－闭空间）

The concepts of countable S-closed spaces and countable para-S-closed are defined, and some properties of them are also studied. The results obtained in P_∑~* space are as follows: in extremely disconnected spaces. countable compact is countable S-closed. countable pare-compact is countable pare-S-closed; in P_∑~* -spaces. countable S-closed is countable compact and extremely disconnected. countable pare-S-closed is countable pare-compact and extremely disconnected; (X ) is countable S-closed (countable pare-S-closed ) spaces. only its semi- regularization (X.) is countable S-closed(countable pare-S- closed).