On the number of Gdelta points in somewhat Lindelof spaces
by
Zoltan Balogh
Miami University, Oxford, OH 45056

Definition. The separable pseudo-character of a space X is the smallest infinite cardinal kappa such that every separable closed subset of X is the intersection of at most kappa many open sets.

Theorem. Suppose that X is a T1-space with no uncountable free sequences and that that the separable pseudo-character of X is at most c. Then (a) d(X) is no bigger than c; (b) X has at most c many Gdelta points.

Strengthenings of results of Arhangel'skii and Buzyakova will be deduced. Extensions to higher cardinals will be presented.

Date received: February 22, 2002