0000000000670786

AUTHOR

J.f. Martínez

showing 2 related works from this author

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.

Countable cover by sets of small local diameterRosenthal compactaRenormingsσ-fragmentabilityTopology and its Applications
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Sigma-fragmentability and the property SLD in C(K) spaces

2009

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.

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