Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

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



Inserted: 20 jul 2023
Last Updated: 20 jul 2023

Year: 2022

ArXiv: 2207.00570 PDF


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.

Credits | Cookie policy | HTML 5 | CSS 2.1