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2012-12-11 Nonlinear Seminar

Monika Naskręcka
Homeomorphism of the space of polynomials and the space of their roots

During this seminar an elementary, topological proof of continuity of the roots of complex polynomials with respect to their roots will be shown. For normed polynomials with complex coefficients and properly defined metric spaces this theorem can be expressed as a homeomorphism of corresponding metric spaces of coeffecients and roots.