*Definition [#zfd643d3]
A ''π-base'' for a topological space X is a collection P of open subsets such that every nonempty open subset U of X contains some nonempty member V in P.
The ''π-weight'' of X, denoted by ''πw(X)'', is the smallest size |B| of a π-base B for X.
Every base is a π-base while the converse is not true.