Roots and Polynomials as Homeomorphic SpacesExpositiones Mathematicae (2006)
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.
- Roots of polynomials,
Publication DateFebruary, 2006
Citation InformationBranko 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/