countably almost-compact

Definition

Let E be a family of open sets and let F denote the family of the closures of all elements in E. A topological space is called almost compact if F has a nonempty intersection whenever E has cip.

Property

• If X is countably almost-compact and almost realcompact then X is almost-compact.

Remark

• It is called H-closed in the terminology of M. Kateiov.

Reference

Zdenek Frolik, A generalization of realcompact spaces, Czechoslovak Mathematical Journal, Vol.13 (1963), No.1, 127-138.