regularly co-compact

Definition

A topological space X is called regularly co-compact if there is a base B for the open sets of X such that for every subfamily C of B, if the closures of the members of C have fip then they have a nonempty intersection.

Reference

• H. Bennett and D. J. Lutzer, Strong completeness properties in topology, Questions and Answers in General Topology, 27(2009), 107-124.
• http://www.math.wm.edu/~lutzer/drafts/BigBushes.pdf (preprint)