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Title: The JNR Property and the Borel Structure of a Banach Space
Authors: Oncina, L.
Keywords: Borel Sets
Countable Cover By Sets Of Small Local Diameter
Topological Invariants Of The Weak Topology
Issue Date: 2000
Publisher: Institute of Mathematics and Informatics
Citation: Serdica Mathematical Journal, Vol. 26, No 1, (2000), 13p-32p
Abstract: 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.
Description: Research partially supported by a grant of Caja de Ahorros del Mediterraneo.
ISSN: 1310-6600
Appears in Collections:Volume 26 Number 1

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