Algebraic approximation preserving dimension

Abstract

We prove that each semialgebraic subset of ${\mathbb{R}}^n$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving dimension holds also for semianalytic sets.

10 pages, 1 figure

References in corpus (1)

• Local algebraic approximation of semianalytic sets