Brouwer不动点改进定理

Improving theorem of two-dimension Brouwer fixed point

Brouwer是拓扑的第一个不动点定理。f是将闭圆盘D映入自身的连续映射,必有不动点,即存在z∈D,使f(z)=z。其后的不动点改进定理,都是借助其它数学工具,证明在二维情形下,不改变Brouwer不动点定理条件,存在z∈D,使f(z)=z^n。文中直接使用Brouwer不动点定理给出二维Brouwer不动点改进定理的证明。这一证明虽比较繁杂,但较为初等,避开使用其它数学工具,使可接受这一理论的群体加大。

Brouwer is the first fixed point theor em pologing topology. The improving theorem followin that means employing other mathematical tools to demonstrate the existence of Brouwer fixed point theorem, without changing the condition of Brouwer fixed point theorem in the case of two dimensions. This paper introduces the direct use of Brouwer fixed point to prove improved theorem of two - dimension Brouwer fixed point.The demonstration proves elementary, even if rather complex and the freedom of other mathematical tools means a more likely acceptance of the theory.