On the structure of non dentable subsets of C(ω^ω^k)

Details On the structure of non dentable subsets of C(ω^ω^k) On the structure of non dentable subsets of C(ω^ω^k)

2011-03-02

arxiv.org/abs/1103.0366v1

Mathematics

Functional Analysis

18 pages,accepted in Studia Mathematica

Scientific paper

It is shown that there is no K closed convex bounded non-dentable subset of C({\omega}^{\omega} ^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({\omega}^{\omega} ^k).

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