A NOTE ON WALLMAN COMPACTIFICATIONS

T3 and T3i spaces are characterized in terms of a Wall man compactifi- cation of a r, space X. For a P, space (X, IT) consider the Wallman compactification (x, (X*, %)) (3) consisting of the set X* of all ultraclosed filters on (X, ?T), the topology % on X* generated by {(/*: U E ?T} where U* = {f E X*: U E ). Theorem 1. JSf is P3i iff X* is completely T2 relative to x(X)-