Borel Sets Countable Cover By Sets Of Small Local Diameter Topological Invariants Of The Weak Topology
Institute of Mathematics and Informatics
Serdica Mathematical Journal, Vol. 26, No 1, (2000), 13p-32p
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.
Research partially supported by a grant of Caja de Ahorros del Mediterraneo.