Strongly almost disjoint sets and weakly uniform bases

Abstract

A combinatorial principle CECA is formulated and its equivalence with GCH+ certain weakenings of Box_lambda for singular lambda is proved. CECA is used to show that certain ``almost point- < tau&#39;&#39; families can be refined to point- < tau families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of ``every first countable T_1-space with a weakly uniform base has a point-countable base.&#39;&#39;