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On the separation of basic semialgebraic sets by polynomials

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Abstract

In this paper we show that two disjoint basic closed semialgebraic sets, defined over a real closed field R, can be separated by a polynomial, if one of them has dimension ≦2. Counterexamples are given in all higher dimensions.

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Authors and Affiliations

  1. Mathematisches Institut der Universität, Einsteinstraße 62, D-4400, Münster

    Ludwig Bröcker

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  1. Ludwig Bröcker
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Bröcker, L. On the separation of basic semialgebraic sets by polynomials. Manuscripta Math 60, 497–508 (1988). https://doi.org/10.1007/BF01258667

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  • DOI: https://doi.org/10.1007/BF01258667

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