*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.