Real Algebraic and Analytic Geometry

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230. Andreas Fischer:
O-minimal analytic separation of sets in dimension two.


Submission: 2007, July 25.

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.

Full text, 12p.: dvi 59k, ps.gz 159k, pdf 203k.

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