*Definition [#wcaf33de]
-Topological space X is said to be countably ν-compact space if every countable ν-open cover of it has a finite sub cover.
*Property [#te77d47b]
-ν-closed subset of a countably ν-compact space is countably ν-compact.
- A ν-irresolute image of a countably ν-compact space is countably ν-compact.
- countable product of countably ν-compact spaces is countably ν-compact.
- countable union of countably ν-compact spaces is countably ν-compact.
-For a  ν-T_1 topological space X the following statements are equivalent
++ X is countably ν-compact.
++ Every countable family of ν-closed subsets of X which has the finite intersection property has a non-empty intersection.
++ Every infinite subset has an ν-accumulation point.
++ Every sequence in X has a ν-limit point.
++ Every infinite ν-open cover has a proper sub cover

*Reference [#ef723114]
-S. Balasubramanian, P. Aruna Swathi Vyjayanthi and C. Sandhya,''ν-Compact spaces '', Scientia Magna, international book series, Vol. 5 (2009), No. 1 (78-82)