Abstract
It is shown that ifB is the unit ball of a non-separable Hilbert space with its weak topology, then for every number λ≧1, there exists a spaceK λ containingB, such that the constant of simultaneous extension fromC(B) toC(K λ) is exactly λ. This gives a negative answer to the question whether the constants of simultaneous extension ought to be odd integers, as was suggested by examples of Corson-Lindenstrauss and Corson-Pelczynski.
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