The convex point of continuity property in Asplund spaces (Q1818989)

A Banach space has the convex point of continuity property (CPCP) if, for every non-empty closed convex subset \(D\) of the unit ball, the identity map on \(D\) has a point of weak-to-norm continuity. The author shows that if \(X\) is an Asplund space then the following are equivalent: \(X\) has the CPCP; each subspace of \(X\) with a basis has the CPCP; each subspace of \(X\) with a shrinking basis has the CPCP.