球面与扩充平面的拓扑同胚

The Topological Mapping Between Sphere and Extended Plane

本文从通常所说的球面与扩充平面(平面上添加一个新元素)间的对应关系入手,得到n维球面与n维扩充空间(n维欧氏空间Rn添加一个新元素)间的同胚关系,并用拓扑学知识阐明n维球面与n维欧氏空间Rn是不可能同胚的.

In this paper, we set up the topological mapping between n-dimensional sphere S^n and extended space R*= R^n , where R^n is n-dimensional Euelid space and R^n is a new element. Moreover, we explain that there exists no topological mapping between n-dimensional sphere S^n and space R^n.