Spaces of continuous functions over Dugundji compacta

Abstract

We show that for every Dugundji compact $K$ of weight aleph one the Banach space $C(K)$ is 1-Plichko and the space $P(K)$ of probability measures on $K$ is Valdivia compact. Combining this result with the existence of a non-Valdivia compact group, we answer a question of Kalenda.

8 pages; corrected

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• Banach spaces with projectional skeletons