Definition
A topological space X is called countably subcompact if there is a base B for open sets in X (which is called a subcompact base) such that for every countable subfamily F of B, if F is a regular filter base then F has a non-empty intersection.
Reference
- Y. Ikeda, Cech-compaleteness and countably subcompactness, Topology Proc. Vol.14, pp.75-87 (1989).