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

Pericles D Pavlakos; Minos Petrakis

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arXiv · 1103.0366

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

Pericles D Pavlakos·Minos Petrakis

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Abstract

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).

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BibTeX RIS

Pericles D Pavlakos, Minos Petrakis. 2011-03-02. On the structure of non dentable subsets of C(ω^ω^k). https://arxiv.org/abs/1103.0366

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