Abstract:
In this paper we prove a theorem more general than the following: ``If (X,\Vert\cdot\Vert) is an L_1-predual, B is any boundary of X and \{x_n:n \in \N\} is any subset of X, then the closure of \{x_n:n \in \N\} with respect to the topology of pointwise convergence on $ B$ is separable with respect to the topology generated by the norm, whenever {\rm Ext}(B_{X^*}) is weak ^* Lindelöf.'' Several applications of this result are also presented.