o-minimal analytic separation of sets in dimension 2

Abstract

We study the Hardy field associated with an o-minimal expansion of the real numbers. If the set of analytic germs is dense in the Hardy field, then we can definably analytically separate sets in R2, and we can definably analytically approximate definable continuous unary functions. A similar statement holds for definable smooth functions. © 2008 Elsevier B.V. All rights reserved.