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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References
H. H. Corson and J. Lindenstrauss,On simultaneous extension of continuous functions Bull. Amer. Math. Soc.71 (1965), 542–545.
A. Pelczynski,Linear extensions, linear averagings, and their application to linear topological classification of spaces of continuous functions, Rozprawy Mathematyczne58 (1968).
Z. Semadeni,Spaces of continuous functions, Warsaw, 1971.
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This is a part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss. I wish to thank Professor Lindenstrauss for his interest and advice.
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Benyamini, Y. Constants of simultaneous extension of continuous functions. Israel J. Math. 16, 258–262 (1973). https://doi.org/10.1007/BF02756705
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DOI: https://doi.org/10.1007/BF02756705