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

Author: Cecília S. Fernandez
Journal: Proc. Amer. Math. Soc. 126 (1998), 2687-2690
MSC (1991): Primary 46B99
MathSciNet review: 1485473
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Abstract | References | Similar Articles | Additional Information

Abstract: We present an example showing that the multilinear version of the Bartle-Graves Selection Theorem is false, even on finite dimensional spaces.

References [Enhancements On Off] (What's this?)

  • R. G. Bartle and L. M. Graves, Mappings Between Function Spaces, Trans. Amer. Math. Soc. 72 (1952), 400-413.
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  • N. Bourbaki, Topological vector spaces. Chapters 1–5, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1987. Translated from the French by H. G. Eggleston and S. Madan. MR 910295
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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

Keywords: Continuous selections, multilinear mappings
Received by editor(s): January 28, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society