A tree characterization of the point of continuity property in general Banach spaces

Abstract

We obtain a characterization of the point of continuity property for general bounded subsets in Banach spaces in terms of trees. For this we introduce the notion of a topologically weakly null tree and, as a consequence, we get that a general Banach space satisfies the point of continuity property if, and only if, every seminormalized topologically weakly null tree has a boundedly complete branch.