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

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Pavlakos P., Petrakis M.

Studia Mathematica

2011

tom 203

nr 3

205-222

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 $C(ω^{ω^{k}})$.

Ograniczanie wyników

1 Studia Mathematica

1 Pavlakos P.

1 Petrakis M.

1 2011

Wyniki wyszukiwania

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