countably base-compact

Definition

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

• Every countably base-compact space is countably subcompact

Reference

• Jiling Cao and Heikki J. K. Junnila, Amsterdam Properties of Wijsman hyperspaces, Proc. Amer. Math. Soc. Vol.138, No.2 (2010), pp.769-776.