*Definition [#nb99630d]
A topological space X is called base-base metacompact if it has an open base B such that every subfamily C in B, which is also base for X, contains a [[point-finite]] subcover.
*Reference [#bb235b3b]
S. G. Popvassilev, ''Base-cover paracompactness'', Proc. Amer. Math. Soc. Vol.132, No.10, pp.3121-3130.