We prove that a continuous image of a Radon-Nikodým compact of weight less than b is Radon-Nikodým compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than 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 b.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-5,
author = {Antonio Avil\'es},
title = {Radon-Nikod\'ym compact spaces of low weight and Banach spaces},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {71-82},
zbl = {1086.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-5}
}
Antonio Avilés. Radon-Nikodým compact spaces of low weight and Banach spaces. Studia Mathematica, Tome 166 (2005) pp. 71-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-1-5/