Representing a differentiable function as a Cartesian product

Colvin, Michael R.

doi:10.1090/S0002-9939-1983-0715879-3

Representing a differentiable function as a Cartesian product
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by Michael R. Colvin PDF

Proc. Amer. Math. Soc. 89 (1983), 523-526 Request permission

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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Sur les équations et les transformations

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