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A counterexample to the Bartle-Graves selection theorem for multilinear maps

Author(s): Cecília S. Fernandez
Journal: Proc. Amer. Math. Soc. 126 (1998), 2687-2690.
MSC (1991): Primary 46B99
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Abstract: We present an example showing that the multilinear version of the Bartle-Graves Selection Theorem is false, even on finite dimensional spaces.

References:

[1]: R. G. Bartle and L. M. Graves, Mappings Between Function Spaces, Trans. Amer. Math. Soc. 72 (1952), 400-413. MR 13:951i
[2]: C. Bessaga and A. Pelczynski, Selected Topics in Infinite Dimensional Topology, Monografie Matematyczne 58, Polish Scientific Publishers, Warszawa (1975). MR 57:17657
[3]: N. Bourbaki, Topological Vector Spaces, Springer-Verlag (1987). MR 88g:46002
[4]: B. P. Palka, An Introduction to Complex Function Theory, Springer-Verlag (1991). MR 92b:30001

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Additional Information:

Cecília S. Fernandez
Affiliation: Departamento de Matemática, Universidade Federal do Espírito Santo, Av. Fernando Ferrari s/n. 29060-900, Vitória, ES, Brasil
Address at time of publication: Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242

DOI: 10.1090/S0002-9939-98-04730-3
PII: S 0002-9939(98)04730-3
Keywords: Continuous selections, multilinear mappings
Received by editor(s): January 28, 1997
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1998, American Mathematical Society


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