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Properties of generic altitude functions

✍ Scribed by Barry A. Peratt; Judy A. Kennedy

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 278 KB
Volume: 106
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00073-5

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✦ Synopsis

Using the typical C 1 -topology, we prove that a generic C 1 function f : K ⊂ R n → R on a compact neighborhood which has a zero gradient point necessarily has a zero-measure Cantor set C on which its gradient vanishes and on which its set of local extrema is dense.

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