Lindelof type of generalization of separability in Banach spaces
Functional Analysis
2008-04-10 v2
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.
Keywords
Cite
@article{arxiv.0803.3541,
title = {Lindelof type of generalization of separability in Banach spaces},
author = {Jarno Talponen},
journal= {arXiv preprint arXiv:0803.3541},
year = {2008}
}