On the structure of non-dentable subsets of $C(\omega ^{\omega ^{{k}}} )$
Volume 203 / 2011
Studia Mathematica 203 (2011), 205-222
MSC: 46B20, 46B22.
DOI: 10.4064/sm203-3-1
Abstract
It is shown that there is no closed convex bounded non-dentable subset $K$ of $C(\omega ^{\omega ^{k}})$ such that on subsets of $K$ the PCP and the RNP are equivalent properties. Then applying the Schachermayer–Rosenthal theorem, we conclude that every non-dentable $K$ contains a non-dentable subset $L$ so that on $L$ the weak topology coincides with the norm topology. It follows from known results that the RNP and the KMP are equivalent on subsets of $C(\omega ^{\omega ^{k}})$.
