In this paper we consider the problem of separating by a polynomial function two open disjoint semi-algebraic subsets A and B of a real affine variety M under the assumption that the subsets are already polynomially separated up to a proper algebraic subset. First of all some elementary results in small dimensions are given. When M is non-singular, a hypothesis on the behaviour of the boundaries of A and B is sufficient to obtain the separation. The problem is also analysed if M is singular, and some positive results are obtained in the compact case.

Separation de semi-algebriques

FORTUNA, ELISABETTA;GALBIATI, MARGHERITA
1989

Abstract

In this paper we consider the problem of separating by a polynomial function two open disjoint semi-algebraic subsets A and B of a real affine variety M under the assumption that the subsets are already polynomially separated up to a proper algebraic subset. First of all some elementary results in small dimensions are given. When M is non-singular, a hypothesis on the behaviour of the boundaries of A and B is sufficient to obtain the separation. The problem is also analysed if M is singular, and some positive results are obtained in the compact case.
Fortuna, Elisabetta; Galbiati, Margherita
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/10989
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