The Point of Continuity Property: Descriptive Complexity and Ordinal Index

Bossard, Benoit, and López, Ginés. "The Point of Continuity Property: Descriptive Complexity and Ordinal Index." Serdica Mathematical Journal 24.2 (1998): 199-214. <http://eudml.org/doc/11590>.

@article{Bossard1998,
abstract = {∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142Let 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.},
author = {Bossard, Benoit, López, Ginés},
journal = {Serdica Mathematical Journal},
keywords = {Point of Continuity Property; Borel Set; Ordinal Index; point of continuity property; Borel set; ordinal index; Effros-Borel structure; oscillation rank; finite-dimensional decomposition; shrinking basis},
language = {eng},
number = {2},
pages = {199-214},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {The Point of Continuity Property: Descriptive Complexity and Ordinal Index},
url = {http://eudml.org/doc/11590},
volume = {24},
year = {1998},
}

TY - JOUR
AU - Bossard, Benoit
AU - López, Ginés
TI - The Point of Continuity Property: Descriptive Complexity and Ordinal Index
JO - Serdica Mathematical Journal
PY - 1998
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 24
IS - 2
SP - 199
EP - 214
AB - ∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142Let 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.
LA - eng
KW - Point of Continuity Property; Borel Set; Ordinal Index; point of continuity property; Borel set; ordinal index; Effros-Borel structure; oscillation rank; finite-dimensional decomposition; shrinking basis
UR - http://eudml.org/doc/11590
ER -