Proceedings of the American Mathematical Society

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

 

 

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
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, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR 0203075
  • [2] John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
  • [3] Morris Marden, Geometry of polynomials, Second edition. Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
  • [4] B. L. van der Waerden, Algebra, I, Ungar, New York, 1970

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Additional Information

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