Real Algebraic and Analytic Geometry

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331. Andreas Fischer:
Approximation of o-minimal maps satisfying a Lipschitz condition.

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Submission: 2011, October 30.

Abstract:
Consider an o-minimal expansion of the real field. We show that definable Lipschitz continuous maps can be definably fine approximated by definable continuously differentiable Lipschitz maps whose Lipschitz constant is close to that of the original map.

Mathematics Subject Classification (2000): 03C64, 14P99, 26B35, 26B05.

Keywords and Phrases: Lipschitz map, Approximation, o-minimal.

Full text, 16p.: dvi 82k, pdf 309k.


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