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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A critical set with nonnull image has large Hausdorff dimension
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by Alec Norton PDF
Trans. Amer. Math. Soc. 296 (1986), 367-376 Request permission

Abstract:

The question of how complicated a critical set must be to have a nonnull image is answered by relating its Hausdorff dimension to the (Hölder) differentiability of the map. This leads to a new extension of the Morse-Sard Theorem. The main tool is an extended version of Morse’s Lemma.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 296 (1986), 367-376
  • MSC: Primary 26B35; Secondary 28A25, 58C25, 58E05
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0837817-2
  • MathSciNet review: 837817