Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/404

 Title: The JNR Property and the Borel Structure of a Banach Space Authors: Oncina, L. Keywords: Borel SetsCountable Cover By Sets Of Small Local DiameterTopological 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. URI: http://hdl.handle.net/10525/404 ISSN: 1310-6600 Appears in Collections: Volume 26 Number 1

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