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On the space of continuous functions on a dyadic set

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  26 February 2010

Grzegorz Plebanek
Grzegorz Plebanek
Affiliation:
Professor Grzegorz Plebanek, Institute of Mathematics, Wroclaw University, Grunwaldzki 2/4, 50384 Wroclaw, Poland.
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Extract

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).

MSC classification

Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 42 - 49
Copyright
Copyright © University College London 1991

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