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arXiv · 2207.00570

Urysohn in action: separating semialgebraic sets by polynomials

Milan Korda·Jean-Bernard Lasserre·Alexey Lazarev·Victor Magron·Simone Naldi
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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.

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Milan Korda, Jean-Bernard Lasserre, Alexey Lazarev, Victor Magron, Simone Naldi. 2022-07-01. Urysohn in action: separating semialgebraic sets by polynomials. https://arxiv.org/abs/2207.00570

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