Real Algebraic and Analytic Geometry
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230. Andreas Fischer:
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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