Topological properties of Banach spaces

Gerald Arthur Edgar and Robert Francis Wheeler

Vol. 115 (1984), No. 2, 317–350

DOI: 10.2140/pjm.1984.115.317

Abstract

Let X be a Banach space, B_X its closed unit ball. We study several topological properties of B_X with its weak topology. In particular, we consider spaces X such that (B_X, weak) is a Polish topological space. If X has RNP and X^∗ is separable, then B_x is Polish; if B_X is Polish, then X is somewhat reflexive. We also consider spaces X such that every closed subset of (B_X, weak) is a Baire space. This is equivalent to property (PC), studied by Bourgain and Rosenthal.

Mathematical Subject Classification 2000

Primary: 46B20

Secondary: 46B10

Milestones

Received: 23 March 1983

Published: 1 December 1984