Real Algebraic and Analytic Geometry |

Zero-Set Property of O-Minimal Indefinitely Peano Differentiable Functions.

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Submission: 2007, January 31.

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

Mathematics Subject Classification (2000): 03C64; 49J52.

Keywords and Phrases: o-minimal structure, Peano differentiable functions, zero-set property.

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