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

Andreas Fischer. "Zero-set property of o-minimal indefinitely Peano differentiable functions." Annales Polonici Mathematici 94.1 (2008): 29-41. <http://eudml.org/doc/280572>.

@article{AndreasFischer2008,
abstract = {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.},
author = {Andreas Fischer},
journal = {Annales Polonici Mathematici},
keywords = {o-minimal structure; Peano differentiable function},
language = {eng},
number = {1},
pages = {29-41},
title = {Zero-set property of o-minimal indefinitely Peano differentiable functions},
url = {http://eudml.org/doc/280572},
volume = {94},
year = {2008},
}

TY - JOUR
AU - Andreas Fischer
TI - Zero-set property of o-minimal indefinitely Peano differentiable functions
JO - Annales Polonici Mathematici
PY - 2008
VL - 94
IS - 1
SP - 29
EP - 41
AB - 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.
LA - eng
KW - o-minimal structure; Peano differentiable function
UR - http://eudml.org/doc/280572
ER -