完备Riemann流形具有闭的割空间

Complete Riemannian Manifolds have the Closed Cut Space

本文证明了完备的Ｒｉｅｍａｎｎ流形即拥有闭的割空间（ｃｕｔｓｐａｃｅ），这一结论不但完满解答了段海豹在［１］中提出的问题１．６，大大地改进了他的主要结果（［１］，定理１．３），而且作为一个推论，我们还得到了经典Ｂｏｒｓｕｋ－Ｕｌａｍ定理的一个进一步推广．

In this paper we prove that complete Riemannian manifolds have the closed cut space. This result not only answers question 1.6 which is proposed by Duan Haibao in and improves his main result (, theorem 1.3), but also as a consequence the generalization of the classical Borsuk-Ulam theorem is obtained.