A critical set with nonnull image has large Hausdorff dimension

Norton, Alec

doi:10.1090/S0002-9947-1986-0837817-2

A critical set with nonnull image has large Hausdorff dimension
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by Alec Norton

Trans. Amer. Math. Soc. 296 (1986), 367-376

DOI: https://doi.org/10.1090/S0002-9947-1986-0837817-2

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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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