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
1989-01-01
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
