Real Algebraic and Analytic Geometry
Submission: 2006, July 18.
Let M be an o-minimal structure over the real closed field R. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable we are even able to preserve the Lipschitz constant.
Mathematics Subject Classification (2000): 03C64, 26B05.
Keywords and Phrases: o-minimal structure, smoothing, Lipschitz continuous function, approximation.
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