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On the structure of non-dentable subsets of $C (ω^{ω^{k}})$

Pericles D. Pavlakos; Minos Petrakis — 2011

Studia Mathematica

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

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

On the structure of non-dentable subsets of $C (ω^{ω^{k}})$