Radon-Nikod\'ym compact spaces of low weight and Banach spaces
A Avilés - arXiv preprint arXiv:1012.5512, 2010 - arxiv.org
arXiv preprint arXiv:1012.5512, 2010•arxiv.org
We prove that a continuous image of a Radon-Nikod\'ym compact space of weight less than
b is Radon-Nikod\'ym 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 which has density character exactly b.
b is Radon-Nikod\'ym 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 which has density character exactly b.
We prove that a continuous image of a Radon-Nikod\'ym compact space of weight less than b is Radon-Nikod\'ym 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 which has density character exactly b.
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