6533b82efe1ef96bd12944c2

RESEARCH PRODUCT

Sigma-fragmentability and the property SLD in C(K) spaces

J.f. Martínez

subject

CombinatoricsDiscrete mathematicsClass (set theory)Property (philosophy)Cover (topology)Metric (mathematics)Banach spaceSigmaCountable setGeometry and TopologyMathematics

description

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.

yearjournalcountryeditionlanguage
2009-04-01Topology and its Applications
https://doi.org/10.1016/j.topol.2008.12.037