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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Representing a differentiable function as a Cartesian product


Author: Michael R. Colvin
Journal: Proc. Amer. Math. Soc. 89 (1983), 523-526
MSC: Primary 55M20
MathSciNet review: 715879
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Abstract: This article produces an elementary proof of a result originally stated without proof by J. Leray. The main result gives conditions so that a continuously differentiable map from a product neighborhood of the origin in $ {{\mathbf{R}}^n}$ into $ {{\mathbf{R}}^n}$ can be homotoped to a cartesian product of maps on intervals. The resulting product function preserves properties of the original map near the origin.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0715879-3
PII: S 0002-9939(1983)0715879-3
Keywords: Fixed point theory, index, jacobian, Whitney extension theorems, inverse function theorem
Article copyright: © Copyright 1983 American Mathematical Society