用组合方法证明三维情况的Brouwer不动点定理

A Combinatorial Proof of the Brouwer Fixed Point Theorem in Three Dimensions

通过使用组合方法,Sperner引理以及拓扑基础性质(连续性,紧致性)以及连续的向量场与连续变换之间的关系,来证明3维情况下,Brouwer不动点定理,给出了有别于以往代数拓扑证明新方法.

Through the using of combinatorial method that contains Sperner Lemma and the using of topology fundamental properties that contain continuity and Compactness,and the relationship between continuous transformation and the corresponding vector field,we provide a new method about the Brouwer fixed point theorem in three dimensions,which is different from the past algebraic topology proofs.