On the topology of pointwise convergence on the boundaries of L1-preduals

Abstract

n this paper we prove a theorem more general than the following: 'If X is an L-1-predual, B is any boundary of X and {x(n) : n is an element of N} is any subset of X, then the closure of {x(n) : n is an element of N} with respect to the topology of pointwise convergence on B is separable with respect to the topology generated by the norm, whenever Ext(B-X*) is weak* Lindelof.' Several applications of this result are also presented.

Keywords

• topology
• pointwise
• convergence
• boundaries
• L1-preduals