Abstract
Given an o-minimal expansion M of a real closed field R which is not poly- nomially bounded. Let P 1 denote the definable indefinitely Peano dierentiable functions. If we further assume that M admits P 1 cell decomposition, each definable closed subset A of R n is the zero-set of a P 1 function f : R n ! R. This implies P 1 approximation of definable continuous functions and gluing of P 1 functions defined on closed definable sets.
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