Brouwer's Contribution To Topology

In the early 20 th century,a series of creative work by Dutch mathematician Brouwer,providing new tools and methods for nascent Topology,solving a number of topological problems that have plagued mathematicians at the turn of the century,laid a solid foundation for the flourishing of topology in the 20 th century.Brouwer also became one of the founders of modern topology which had the same status as Poincaré.Based on the collection,collation and analysis of relevant literatures,combined with the early history of the development of topological problems,this thesis systematically combs Brouwer's topological results and explores the generation of Brouwer's topological methods and ideas and its impact on his inheritor,to make sure that Brouwer's contribution to topology is fully and deeply understood.The main results obtained are as follows:1.Brouwer's life is described in detail.His life can be divided into three stages: “school time”,“the special research period of topology”,and “the period of returning to mathematics foundation”.At the same time,the social environment at that time and the intuitionistic view held by himself were the main reasons that led to the change of Brouwer's interest in mathematical research in different periods.2.This thesis Outlines the background and early work of Brouwer's topological research,and compares him with Poincare.Poincare's discussion of "Analysis situs" defined the research object and development framework for combinatorial topology,and Brouwer provided a method for proving the correctness of many conclusions in combinatorial topology.Both of them opened the way for the development of topology in the 20 th century.3.The process of Brouwer's topological thoughts and methods is explored,and his contribution for Topology is comprehensively combed.The process of generating new concepts and methods such as mapping degree and simplicial approximation is examined in detail.According to the time and logical relationship between various problems,this thesis introduces many topological problems solved by Brouwer with new tools.Finally,it focuses on the generation and development of Brouwer's fixed point theorem which is classic and widely used until today,and the strict definition of the dimension that Brouwer first gave.4.This thesis expounds the influence of Brouwer's thoughts of topology and methods on the subsequent topologists,and introduces several mathematicians' work related to the use of Brouwer's method to make a breakthrough contribution to the development of topology.It is clear that Brouwer is the founder of topology.