*Definition [#e0858c03]
A quasi-regular space X (i.e. for every nonempty open subset U, there is a nonempty open subset V whose closure is contained in U) is called almost countably base-compact if there is a [[π-base]] B 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 [#n9ce9aad]
-Every almost countably base-compact space is [[almost countably subcompact]]
*Reference [#sc6f4569]
-Jiling Cao and Heikki J. K. Junnila, ''Amsterdam Properties of Wijsman hyperspaces'', Proc. Amer. Math. Soc. Vol.138, No.2 (2010), pp.769-776.