## M. Korda - J. B. Lasserre - A. Lazarev - V. Magron - S. Naldi

# Urysohn in action: separating semialgebraic sets by polynomials

created by naldi on 20 Jul 2023

[

BibTeX]

*preprint*

**Inserted:** 20 jul 2023

**Last Updated:** 20 jul 2023

**Year:** 2022

**Abstract:**

A classical result from topology called Uryshon's lemma asserts the existence
of a continuous separator of two disjoint closed sets in a sufficiently regular
topological space. In this work we make a search for this separator
constructive and efficient in the context of real algebraic geometry. Namely,
given two compact disjoint basic semialgebraic sets which are contained in an
$n$-dimensional box, we provide an algorithm that computes a separating
polynomial greater than or equal to 1 on the first set and less than or equal
to 0 on the second one.