*Definition [#cc605bd9]
A regular space X is called countably base-compact if there is a base B for open sets of X such that for every countable subfamily C of B with [[fip]], the closures of the members of C have a nonempty intersection.
*Remark [#aeca3339]
-Every countably base-compact space is [[countably subcompact]]
*Reference [#ne48ce23]
-Jiling Cao and Heikki J. K. Junnila, ''Amsterdam Properties of Wijsman hyperspaces'', Proc. Amer. Math. Soc. Vol.138, No.2 (2010), pp.769-776.