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Roots and polynomials as Homeomorphic spaces

Authors
Journal
Expositiones Mathematicae
0723-0869
Publisher
Elsevier
Publication Date
Volume
24
Issue
1
Identifiers
DOI: 10.1016/j.exmath.2005.07.001
Keywords
  • Roots Of Polynomials
  • Continuity
  • Homeomorphism
Disciplines
  • Mathematics

Abstract

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.

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