This is an announcement for the paper "Lindelof type of generalization of separability in Banach spaces" by Jarno Talponen.

Abstract: We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset \mathcal{F} of X^{\ast}, which separates X, there exists a countable separating subset \mathcal{F}_{0} of \mathcal{F}. All separable Banach spaces have CSP and plenty of examples of non-separable CSP spaces are provided. Connections of CSP with Markucevic-bases, Corson property and related geometric issues are discussed.

Archive classification: math.FA

Mathematics Subject Classification: 46B26; 46A50

The source file(s), csp.tex: 62263 bytes, is(are) stored in gzipped form as 0803.3541.gz with size 17kb. The corresponding postcript file has gzipped size 108kb.

Submitted from: talponen@cc.helsinki.fi

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http://front.math.ucdavis.edu/0803.3541

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http://arXiv.org/abs/0803.3541

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