Defining the smooth points of a quotient in polynomially bounded o -minimal structures

Abstract

Working in a polynomially bounded o-minimal structure over R, we prove a 'Tamm property' for quotients of smooth definable functions. For sufficiently large N , the smooth points and the C N points of the quotient coincide. We use standard properties of these structures and a consequence of resolution of singularities.

On Division of Quasianalytic Function Germs

“…Finally, let us mention that the quasianalytic division theorem and formal divisibility was also studied in papers [2,12].…”