The JNR Property and the Borel Structure of a Banach Space

Oncina, L.. "The JNR Property and the Borel Structure of a Banach Space." Serdica Mathematical Journal 26.1 (2000): 13-32. <http://eudml.org/doc/11477>.

@article{Oncina2000,
abstract = {Research partially supported by a grant of Caja de Ahorros del Mediterraneo.In this paper we study the property of having a countable cover by sets of small local diameter (SLD for short). We show that in the context of Banach spaces (JNR property) it implies that the Banach space is Cech-analytic. We also prove that to have the JNR property, to be σ- fragmentable and to have the same Borel sets for the weak and the norm topologies, they all are topological invariants of the weak topology. Finally, by means of “good” injections into c0 (Γ), we give a great class of Banach spaces with the JNR property.},
author = {Oncina, L.},
journal = {Serdica Mathematical Journal},
keywords = {Borel Sets; Countable Cover By Sets Of Small Local Diameter; Topological Invariants Of The Weak Topology; Banach spaces; JNR property; Borel sets; countable cover of small local diameter; topological invariants of the weak topology; -fragmentable; countable cover by sets of small local diameters; SLD-property; Kadets-norm; descriptive Banach space; SLD-map},
language = {eng},
number = {1},
pages = {13-32},
publisher = {Institute of Mathematics and Informatics},
title = {The JNR Property and the Borel Structure of a Banach Space},
url = {http://eudml.org/doc/11477},
volume = {26},
year = {2000},
}

TY - JOUR
AU - Oncina, L.
TI - The JNR Property and the Borel Structure of a Banach Space
JO - Serdica Mathematical Journal
PY - 2000
PB - Institute of Mathematics and Informatics
VL - 26
IS - 1
SP - 13
EP - 32
AB - Research partially supported by a grant of Caja de Ahorros del Mediterraneo.In this paper we study the property of having a countable cover by sets of small local diameter (SLD for short). We show that in the context of Banach spaces (JNR property) it implies that the Banach space is Cech-analytic. We also prove that to have the JNR property, to be σ- fragmentable and to have the same Borel sets for the weak and the norm topologies, they all are topological invariants of the weak topology. Finally, by means of “good” injections into c0 (Γ), we give a great class of Banach spaces with the JNR property.
LA - eng
KW - Borel Sets; Countable Cover By Sets Of Small Local Diameter; Topological Invariants Of The Weak Topology; Banach spaces; JNR property; Borel sets; countable cover of small local diameter; topological invariants of the weak topology; -fragmentable; countable cover by sets of small local diameters; SLD-property; Kadets-norm; descriptive Banach space; SLD-map
UR - http://eudml.org/doc/11477
ER -