An algebraic proof of the Borsuk-Ulam theorem for polynomial mappings
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- by Manfred Knebusch PDF
- Proc. Amer. Math. Soc. 84 (1982), 29-32 Request permission
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 ${S^n}(R) \subset {R^{n + 1}}$.References
- Z. D. Dai, T. Y. Lam, and C. K. Peng, Levels in algebra and topology, Bull. Amer. Math. Soc. (N.S.) 3 (1980), no. 2, 845–848. MR 578376, DOI 10.1090/S0273-0979-1980-14826-0 H. Delfs and M. Knebusch, Semialgebraic topology. II. Basic theory of semialgebraic spaces, Math. Z. (to appear).
Additional Information
- © Copyright 1982 American Mathematical Society
- 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