同胚空间的根与多项式
Roots and polynomials as homeomorphic spaces
摘要：
我们提供了一个统一的，初等的，拓扑方法的经典结果，说明连续性的复根的多项式的系数，和连续性的系数的根。事实上，赋予固定次数的首一多项式空间$n$和$n$根空间适当的拓扑，我们能够以同胚的形式来表述经典定理。相关的拓扑事实也被认为是。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
