An elementary example of Sard's Theorem sharpness

2022/02/16 by Juan Ferrera, J. Mariano Ferrera, Ferrera, Juan
Mathematics · #Mathematical Dynamics and Fractals #math.CA #msc:26B35 #msc:28A75

paper · pdf · doi:10.48550/arxiv.2202.08000

4 pages note-

arxiv created 2022/02/16 · arxiv updated 2022/02/17

Abstract

In this note we define a C¹ function F:[0,M]²→ [0,2] that satisfies that its set of critical values has positive measure. This function provides an example, easier than those that usually appear in the literature, of how the order of differentiability required in Sard's Theorem cannot be improved

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