An elementary example of Sard's Theorem sharpness
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 impro...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71710 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71710 |
| Access Level: | acceso abierto |
| Palabra clave: | 517 Morse-Sard Theorem Cantor set Matemáticas (Matemáticas) Análisis matemático 12 Matemáticas 1202 Análisis y Análisis Funcional |
| Sumario: | 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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