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The roots of a polynomial vary continuously as a function of the coefficients


Authors: Gary Harris and Clyde Martin
Journal: Proc. Amer. Math. Soc. 100 (1987), 390-392
MSC: Primary 30C15; Secondary 26C10, 54B15
DOI: https://doi.org/10.1090/S0002-9939-1987-0884486-8
Addendum: Proc. Amer. Math. Soc. 102 (1988), 993-994.
MathSciNet review: 884486
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Abstract: We present an elementary topological proof that the roots of a polynomial vary continuously as a function of the coefficients.


References [Enhancements On Off] (What's this?)

  • [1] Lars Hörmander, An introduction to complex analysis in several variables, Van Nostrand, New York, 1966 MR 0203075 (34:2933)
  • [2] John Kelley, General topology, Van Nostrand, New York, 1955 MR 0070144 (16:1136c)
  • [3] Morris Marden, Geometry of polynomials, Math. Surveys, no. 3, Amer. Math. Soc., Providence, R.I., 1966 MR 0225972 (37:1562)
  • [4] B. L. van der Waerden, Algebra, I, Ungar, New York, 1970

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0884486-8
Article copyright: © Copyright 1987 American Mathematical Society

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