Real Algebraic and Analytic Geometry |

O-minimal analytic separation of sets in dimension two.

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Submission: 2007, July 25.

*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 analytic separate sets in $\mathbb{R}^2$,
and we can definably analytic approximate definable continuous unary functions.*

Mathematics Subject Classification (2000): 03C64.

Keywords and Phrases: o-minimal structure, analytic separation of sets.

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