基于拓扑度的代数基本定理的证明

Proof of the Fundamental Theorem of Algebra Based on Topological Degree

本文用拓扑度理论给出了代数基本定理的证明。 首先构造同伦方程,把复杂问题约化成一个简单问题;通过对同伦方程所有解的先验界估计,构造出有界开集;最后利用拓扑度的同伦不变性和存在性定理,给出定理的证明。

In the paper, proof of fundamental theorem of algebra is obtained by topological degree theory. Frist we construct a homotopy equation, which can reduce a complex problem into a simpler one. Through a priori estimate for the possible solutions of homotopy equation, we gain a bounded open set;then we prove the theorem by the homotopy invariance and existence theorem of topological degree.