代数基本定理的拓扑证明及推广  

A TOPOLOGICAL PROOF AND GENERALIZATION FOR FUNDAMENTAL THEOREM OF ALGEBRA

作　　者：孙艳红[1] 高会双[1] SUN Yan-hong;GAO Hui-shuang(College of Mathematics,Inner Mongolia University for Nationalities,Tongliao,Inner Mongolia 028000,China)

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028000

出　　处：《井冈山大学学报（自然科学版）》2018年第4期17-20,共4页Journal of Jinggangshan University (Natural Science)

基　　金：内蒙古自治区自然科学基金项目(2016MS0118);内蒙古民族大学校级项目(NMDYB15020)

摘　　要：拓扑学是一个新兴的数学分支,用于研究拓扑空间在连续映射下的性质。20世纪后,拓扑学发展为数学中一个非常重要的领域,拥有大量重大成果:代数拓扑学中的庞加莱猜想的证明是新世纪最瞩目的数学成果;拓扑学在数学其他领域、物理学、化学、生物学、计算机科学、经济学中都有广泛的应用。文中主要给出代数基本定理的代数拓扑方法的证明及推广,并得出了一种复空间上的不动点原理。Topology is a rising branch of Mathematics, which studies the properties of topological spaces under continuous mappings. After twentieth Century, the topology has become a very important field in Mathematics, and it has a lot of significant results. The proof of Poincare＇s conjecture in algebraic topology is the most remarkable achievement in the new century; Topology is widely used in other areas of mathematics, topology, physics, chemistry, biology, computer science and Economics. Fundamental theorem of algebra was proved and expanded by algebraic topology in this article,and then we obtained the fixed point theorem on complex space.

关 键 词：拓扑 同伦 基本群 代数基本定理化 

分 类 号：O152[理学—数学]