## A note on hyperplane sections of real algebraic sets

Gamboa Mutuberria, José Manuel (1984) A note on hyperplane sections of real algebraic sets. Boletín de la Sociedad Matemática Mexicana, 29 (2). pp. 59-63. ISSN 1405-213X

The author studies the size of the set of hyperplanes which meet a non- zero-dimensional algebraic set V over a real-closed ground field R. More precisely, let us denote by $V\sb c$ the locus of central points of V, i.e., the closure, in the order topology of $R\sp n$, of the set of regular points of V. The author proves the following: There exists a linear isomorphism $\sigma$ of $R\sp n$ such that for every generic'' hyperplane H of $R\sp n$, either H meets $V\sb c$ or its transform by $\sigma$ meets $V\sb c$.