Volume 27, Number 1, 2001
DESCRIPTIVE SETS AND THE TOPOLOGY
OF NONSEPARABLE BANACH SPACES
R. W. Hansell firstname.lastname@example.org
2000 Mathematics Subject Classification: 46B20, 54E99, 54H05. Key words: s-scattered network, descriptive Banach space, s-fragmented space.
We call a Banach space descriptive (almost descriptive) if its weak topology has a s-relatively discrete (s-scattered) network. A key property in deriving many of our results is the fact that whenever the weak topology has a network of either type, then the norm topology will have a network of the same type where the discreteness property is again with respect to the weak topology. Properties known to hold for Banach spaces with an equivalent Kadec norm are shown to hold for the more general class of descriptive Banach spaces. And almost descriptive Banach spaces are shown to coincide with s-fragmented Banach spaces introduced by Jayne, Namioka and Rogers.
2000 Mathematics Subject Classification: 35L65, 35L67. Key words: Blow-up, hyperbolic systems.