0000000000739775
AUTHOR
J.f. Martínez
Sigma-fragmentability and the property SLD in C(K) spaces
AbstractWe characterize two topological properties in Banach spaces of type C(K), namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that Cp(K) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in Cp(K) in case K is scattered.
Sigma-fragmentability and the property SLD in C(K) spaces
Abstract We characterize two topological properties in Banach spaces of type C ( K ) , namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that C p ( K ) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in C p ( K ) in case K is scattered.