On the structure of non dentable subsets of C(ω^ω^k)
It is shown that there is no K closed convex bounded non-dentable subset of C(ω^ω ^k) such that on the subsets of K the PCP and the RNP are equivalent properties. Then applying Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains non-dentable subset L so that on L the weak topology coincides with the norm one. It follows from known results that the RNP and the KMP are equivalent properties on the subsets of C(ω^ω ^k).
math.FA↗