Representing a differentiable function as a Cartesian product
HTML articles powered by AMS MathViewer
- by Michael R. Colvin
- Proc. Amer. Math. Soc. 89 (1983), 523-526
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715879-3
- PDF | 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.References
- Ralph Abraham and Joel Robbin, Transversal mappings and flows, W. A. Benjamin, Inc., New York-Amsterdam, 1967. An appendix by Al Kelley. MR 0240836
- Robert F. Brown, An elementary proof of the uniqueness of the fixed point index, Pacific J. Math. 35 (1970), 549–558. MR 281197
- Robert F. Brown, The Lefschetz fixed point theorem, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0283793
- Robert F. Brown, Notes on Leray’s index theory, Advances in Math. 7 (1971), 1–28. MR 296933, DOI 10.1016/0001-8708(71)90040-5 S. Leray, Sur les équations et les transformations, J. Math. Pures Appl. 24 (1945), 201-248.
- Hassler Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), no. 1, 63–89. MR 1501735, DOI 10.1090/S0002-9947-1934-1501735-3
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 89 (1983), 523-526
- MSC: Primary 55M20
- DOI: https://doi.org/10.1090/S0002-9939-1983-0715879-3
- MathSciNet review: 715879