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Some remarks on universality properties of / c

Mikołaj Krupski, Witold Marciszewski (2012)

Colloquium Mathematicae

We prove that if is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into / c . We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into / c , but fails to embed isometrically....

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