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A critical set with nonnull image has large Hausdorff dimension


Author: Alec Norton
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1986-0837817-2
Article copyright: © Copyright 1986 American Mathematical Society

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