Smith特殊指数与Borsuk-Ulam型定理

Smith's Special Index and Borsuk-Ulam Type Theorems

本文利用Smith周期交换理论,给出了带有无定点周期变换的拓扑空间的Smith特殊指数的计算和若干Borsuk-Ulam型定理。

In this paper, we prove some theorems about special computation of the Smith's special index of fixed point free periodic transformations on topology, and some Borsuk-Ulam type theorems.Theorem1.1 Let t be a transformation of period n on topological space X without fixed point,G is any cyclic group, then there exists a resolution of n, n=αβ~k where, β is prime, (α, β)=1. Such that, Smith's special indexTheorem2.2 Let X,Y be Hausdorff space, and let t be a transformation of period n on X without fixed point, n=p_1,…,p_m, p_i is prime (p_i,p_j)=1,1≤i,j≤m, If then, there are m points x_1,…; x_m∈X such that where 1≤i≤m