Proceedings of the London Mathematical Society · 1993 · 55 citations · 0 references
Natural SciencesMathematicsSet TheorySpace TheoryTopologyGeneral TopologyTopological SpacesBaire SpacesSeparable SpacesWeak Topology
Weakly compact sets in Banach spaces are fragmentable. We introduce the weaker notion of the σ-fragmentability of a subset of a Banach space, a notion that has a far wider range of applicability. We prove that all weakly Čech-analytic subsets of a Banach space are σ-fragmented. This implies that all Banach spaces having Kadec norms are σ-fragmented. However l∞ is not σ-fragmented.