*Definition [#m42516fd]
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 [#f4d9b473]
S. G. Popvassilev, ''Base-cover paracompactness'', Proc. Amer. Math. Soc. Vol.132, No.10, pp.3121-3130.