Real Algebraic and Analytic Geometry

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18. F. Broglia, F. Pieroni:
Separation of global semianalytic subsets of 2-dimensional analytic manifolds.


Submission: 2002, October 18.

In this paper we prove that two global semianalytic subsets of a real analytic manifold of dimension two are separable if and only if there is no analytic component of the Zariski closure of the boundary which intersects the interior of one of the two sets and they are separable in a neighbourhood of each singular point of the boundary . Unlike the algebraic case for the same problem, we show that the obstructions at infinity do never appear.

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