Zero-set property of o-minimal indefinitely Peano differentiable functions
Andreas Fischer
Annales Polonici Mathematici, Tome 93 (2008), p. 29-41 / Harvested from The Polish Digital Mathematics Library
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Given an o-minimal expansion ℳ of a real closed field R which is not polynomially bounded. Let ∞ denote the definable indefinitely Peano differentiable functions. If we further assume that ℳ admits ∞ cell decomposition, each definable closed subset A of Rⁿ is the zero-set of a ∞ function f:Rⁿ → R. This implies ∞ approximation of definable continuous functions and gluing of ∞ functions defined on closed definable sets.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:280572 
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Andreas Fischer. Zero-set property of o-minimal indefinitely Peano differentiable functions. Annales Polonici Mathematici, Tome 93 (2008) pp. 29-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-1-3/