An elementary example of Sard's Theorem sharpness

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Ferrera Cuesta, Juan (2022) An elementary example of Sard's Theorem sharpness. (Unpublished)

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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.


Item Type:Article
Uncontrolled Keywords:Morse-Sard Theorem; Cantor set
Subjects:Sciences > Mathematics
Sciences > Mathematics > Mathematical analysis
ID Code:73268
Deposited On:30 Jun 2022 10:02
Last Modified:30 Jun 2022 10:41

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