Roots and polynomials as homeomorphic spaces

Branko Ćurgus; Vania Mascioni

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arXiv · math/0502037

Roots and polynomials as homeomorphic spaces

Branko Ćurgus·Vania Mascioni

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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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BibTeX RIS

Branko Ćurgus, Vania Mascioni. 2005-02-01. Roots and polynomials as homeomorphic spaces. https://arxiv.org/abs/math/0502037

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