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 into can be homotoped to a cartesian product of maps on intervals. The resulting product function preserves properties of the original map near the origin.

**[AR]**Ralph Abraham and Joel Robbin,*Transversal mappings and flows*, An appendix by Al Kelley, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR**0240836****[B]**Robert F. Brown,*An elementary proof of the uniqueness of the fixed point index*, Pacific J. Math.**35**(1970), 549–558. MR**0281197****[B]**Robert F. Brown,*The Lefschetz fixed point theorem*, Scott, Foresman and Co., Glenview, Ill.-London, 1971. MR**0283793****[B]**Robert F. Brown,*Notes on Leray’s index theory*, Advances in Math.**7**(1971), 1–28. MR**0296933****[Le]**S. Leray,*Sur les équations et les transformations*, J. Math. Pures Appl.**24**(1945), 201-248.**[W]**Hassler Whitney,*Analytic extensions of differentiable functions defined in closed sets*, Trans. Amer. Math. Soc.**36**(1934), no. 1, 63–89. MR**1501735**, 10.1090/S0002-9947-1934-1501735-3

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0715879-3

Keywords:
Fixed point theory,
index,
jacobian,
Whitney extension theorems,
inverse function theorem

Article copyright:
© Copyright 1983
American Mathematical Society