regular filter base

Definition

A collection F of nonempty sets is a regular filter base provided that for all F_1 and F_2 in F there is some F_3 in F such that the closure of F_3 is contained in both of F_1 and F_2

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)