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Counterexample to the Morse-Sard theorem in the case of infinite-dimensional manifolds


Author: Ivan Kupka
Journal: Proc. Amer. Math. Soc. 16 (1965), 954-957
MSC: Primary 57.55; Secondary 57.50
DOI: https://doi.org/10.1090/S0002-9939-1965-0182024-4
MathSciNet review: 0182024
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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. 40 (1939), 62-70. MR 1503449
  • [2] Arthur Sard, The measure of the critical values of differentiable maps, Bull. Amer. Math. Soc. 48 (1942), 883-890. MR 0007523 (4:153c)
  • [3] H. Whitney, A function not constant on a connected set of its critical points, Duke Math. J. 1 (1935), 514-517. MR 1545896

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DOI: https://doi.org/10.1090/S0002-9939-1965-0182024-4
Article copyright: © Copyright 1965 American Mathematical Society

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