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  1. O-minimal analytic separation of sets in dimension 2.Andreas Fischer - 2009 - Annals of Pure and Applied Logic 157 (2-3):130-138.
    We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in , and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions.
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  • Infinitely Peano differentiable functions in polynomially bounded o-minimal structures.Andreas Fischer - 2010 - Annals of Pure and Applied Logic 161 (12):1520-1524.
    Let be an o-minimal expansion of a real closed field. We show that the definable infinitely Peano differentiable functions are smooth if and only if is polynomially bounded.
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  • Approximation of o-minimal maps satisfying a Lipschitz condition.Andreas Fischer - 2014 - Annals of Pure and Applied Logic 165 (3):787-802.
    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.
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