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Article
Roots and Polynomials as Homeomorphic Spaces
Expositiones Mathematicae (2006)
  • Branko Ćurgus, Western Washington University
  • Vania Mascioni
Abstract
We provide a unified, elementary, topological approach to the classical results stating the continuity of the complex roots of a polynomial with respect to its coefficients, and the continuity of the coefficients with respect to the roots. In fact, endowing the space of monic polynomials of a fixed degree n and the space of n roots with suitable topologies, we are able to formulate the classical theorems in the form of a homeomorphism. Related topological facts are also considered.
Keywords
  • Roots of polynomials,
  • Continuity,
  • Homeomorphism
Disciplines
Publication Date
February, 2006
Publisher Statement
Published by Elsevier DOI:10.1016/j.exmath.2005.07.001
Citation Information
Branko Ćurgus and Vania Mascioni. "Roots and Polynomials as Homeomorphic Spaces" Expositiones Mathematicae Vol. 24 Iss. 1 (2006)
Available at: http://works.bepress.com/branko_curgus/24/