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On the space of continuous functions on a dyadic set
Published online by Cambridge University Press: 26 February 2010
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In the part (16-3) of his extensive study on measurability in Banach spaces, Talagrand [12] considered the Banach space C(K) of continuous functions on a dyadic topological space K. He proved that C(K) is realcompact in its weak topology, if, and only if, the topological weight of K is not a twomeasurable cardinal (Theorem 16-3-1). Then he asked for an alternative to a rather complicated proof presented there (p. 214) and posed the problem whether C(K) is measure-compact whenever the weight of K is not a realmeasurable cardinal (Problem 16-3-2).
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- Copyright © University College London 1991
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