The Point of Continuity Property: Descriptive Complexity and Ordinal Index
Serdica Mathematical Journal, Tome 24 (1998) no. 2, pp. 199-214
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
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.
Keywords:
Point of Continuity Property, Borel Set, Ordinal Index
@article{SMJ2_1998_24_2_a6,
author = {Bossard, Benoit and L\'opez, Gin\'es},
title = {The {Point} of {Continuity} {Property:} {Descriptive} {Complexity} and {Ordinal} {Index}},
journal = {Serdica Mathematical Journal},
pages = {199--214},
publisher = {mathdoc},
volume = {24},
number = {2},
year = {1998},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_1998_24_2_a6/}
}
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 SP - 199 EP - 214 VL - 24 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SMJ2_1998_24_2_a6/ LA - en ID - SMJ2_1998_24_2_a6 ER -
Bossard, Benoit; López, Ginés. The Point of Continuity Property: Descriptive Complexity and Ordinal Index. Serdica Mathematical Journal, Tome 24 (1998) no. 2, pp. 199-214. http://geodesic.mathdoc.fr/item/SMJ2_1998_24_2_a6/