ABSTRACT
A filterbase in a set Y is a nonempty set T of nonempty subsets of Y such that given members A, B of T there is some member C which is contained in both A and B. By induc tion the intersection of finitely many members of T contains a member of T. A subset E of Y is cofinal for E if E meets every member of E. E is te rm in a l for E if E contains a mem ber of E. E is cofinal if and only if its complement Y — E is not terminal. A property of points in Y holds frequen tly if it holds at every point in some cofinal set; it holds u ltim ate ly if it holds at every point in some terminal set. These two con cepts behave like existential and universal quantifiers. They reduce to these for the trivial filterbase having Y as its only member.
