Zero-set property of $o$-minimal indefinitely Peano differentiable functions

Volume 94 / 2008

Andreas Fischer Annales Polonici Mathematici 94 (2008), 29-41 MSC: Primary 03C64; Secondary 14P10. DOI: 10.4064/ap94-1-3

Abstract

Given an $o$-minimal expansion $\mathcal M$ of a real closed field $R$ which is not polynomially bounded. Let $\mathcal {TP}^\infty$ denote the definable indefinitely Peano differentiable functions. If we further assume that $\mathcal M$ admits $\mathcal {TP}^{\infty}$ cell decomposition, each definable closed subset $A$ of $R^n$ is the zero-set of a $\mathcal {TP}^{\infty}$ function $f:R^n\rightarrow R$. This implies $\mathcal {TP}^\infty$ approximation of definable continuous functions and gluing of $\mathcal {TP}^\infty$ functions defined on closed definable sets.

Authors

  • Andreas FischerDepartment of Mathematics & Statistics
    University of Saskatchewan
    106 Wiggins Road
    Saskatoon, SK, S7N 5E6, Canada
    e-mail

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