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Transactions of the American Mathematical Society

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On the existence of functions having given partial derivatives on a curve


Author: Maurice Sion
Journal: Trans. Amer. Math. Soc. 77 (1954), 179-201
MSC: Primary 27.2X
DOI: https://doi.org/10.1090/S0002-9947-1954-0064846-0
MathSciNet review: 0064846
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References [Enhancements On Off] (What's this?)

  • [1] A. P. Morse, The behavior of a function on its critical set, Ann. of Math. vol. 40 (1939) pp. 62-70. MR 1503449
  • [2] A. Sard, The measure of the critical values of differentiable maps, Bull. Amer. Math. Soc. vol. 48 (1942) pp. 883-890. MR 0007523 (4:153c)
  • [3] H. Whitney, Analytic extensions of differentiable functions defined on closed sets, Trans. Amer. Math. Soc. vol. 36 (1934) pp. 63-89. MR 1501735
  • [4] -, A function not constant on a connected set of critical points, Duke Math. J. vol. 1 (1935) pp. 514-517. MR 1545896
  • [5] W. M. Whyburn, Non-isolated critical points of functions, Bull. Amer. Math. Soc. vol. 35 (1929) pp. 701-708. MR 1561794

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DOI: https://doi.org/10.1090/S0002-9947-1954-0064846-0
Article copyright: © Copyright 1954 American Mathematical Society

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