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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An algebraic proof of the Borsuk-Ulam theorem for polynomial mappings


Author: Manfred Knebusch
Journal: Proc. Amer. Math. Soc. 84 (1982), 29-32
MSC: Primary 14G30; Secondary 12D15, 55M20
DOI: https://doi.org/10.1090/S0002-9939-1982-0633271-6
MathSciNet review: 633271
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Abstract: An algebraic proof is given for the following theorem: Every system of $ n$ odd polynomials in $ n + 1$ variables over a real closed field $ R$ has a common zero on the unit sphere $ {S^n}(R) \subset {R^{n + 1}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0633271-6
Article copyright: © Copyright 1982 American Mathematical Society