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Title: The Point of Continuity Property: Descriptive Complexity and Ordinal Index
Authors: Bossard, Benoit
López, Ginés
Keywords: Point of Continuity Property
Borel Set
Ordinal Index
Issue Date: 1998
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 24, No 2, (1998), 199p-214p
Abstract: Let X be a separable Banach space without the Point of Continuity Property. When the set of closed subsets of its closed unit ball is equipped with the standard Effros-Borel structure, the set of those which have the Point of Continuity Property is non-Borel. We also prove that, for any separable Banach space X, the oscillation rank of the identity on X (an ordinal index which quantifies the Point of Continuity Property) is determined by the subspaces of X with a finite-dimensional decomposition. If X does not contain l1 , subspaces with basis suffice. If X ∗ is separable, one can even restrict to subspaces with shrinking basis.
Description: ∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142
ISSN: 1310-6600
Appears in Collections:Volume 24 Number 2

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