Real Algebraic and Analytic Geometry |

On connected components of some globally semi-analytic sets.

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Submission: 2011, May 19.

*Abstract:
We isolate a class, say $\mathcal{A}$, of global real analytic functions such that, each global semi-analytic set defined by
$\mathcal{A}$ has only finitely many connected components and each component is also a global semi-analytic set defined by
$\mathcal{A}$.*

Mathematics Subject Classification (2010): 14B25, 14B10, 32B05, 32B20, 03C10.

Keywords and Phrases: Weierstrass division theorem, semi-analytic sets, o-minimal structures.

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