base-base paracompact

Definition

A topological space X is called base-base paracompact if it has an open base B such that every subfamily C in B, which is also base for X, contains a locally finite subcover.

Reference

S. G. Popvassilev, Base-cover paracompactness, Proc. Amer. Math. Soc. Vol.132, No.10, pp.3121-3130.