摘要
本文应用Ｓｍｉｔｈ周期变换理论，根据球面在周期变换下的指数，对球面上的点在连续映射下的性质作了进一步探讨，从而丰富了ＢｏｒｓｕｋＵｌａｍ定理．
The property of the point on sphere under continuous mapping is discussed with Smith cycle transformation theory and the index under cycle transformation on sphere. Then the Borsuk Ulam theorem is extended widely.
关键词
周期变换
协变映射
连续映射
球面
点
Smith specical index, cycle transformation, covariant map.
