Radon–Nikodým compact spaces of low weight and Banach spaces
Volume 166 / 2005
Studia Mathematica 166 (2005), 71-82
MSC: Primary 46B26; Secondary 46B22, 46B50, 54G99.
DOI: 10.4064/sm166-1-5
Abstract
We prove that a continuous image of a Radon–Nikodým compact of weight less than ${\bf b}$ is Radon–Nikodým compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than ${\bf b}$ are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated and which has density character exactly ${\bf b}$.
