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π-base

Last-modified: 2011-03-19 (土) 00:20:22

Definition Edit

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.