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

• Autorzy: Andreas Fischer
• Języki publikacji: EN

Abstrakty

EN

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 subset A of Rⁿ is the zero-set of a $𝓟^{∞}$ function f:Rⁿ → R. This implies $𝓟^{∞}$ approximation of definable continuous functions and gluing of $𝓟^{∞}$ functions defined on closed definable sets.

Kategorie tematyczne

• 03C64: Model theory of ordered structures; o-minimality
• 14P10: Semialgebraic sets and related spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 1
• Strony: 29-41

Daty

wydano

2008

Twórcy

autor

Andreas Fischer

• Department of Mathematics & Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada

Identyfikatory

DOI

10.4064/ap94-1-3