1·This paper tries to define metric function for homeomorphic mapping, and a sufficient condition of bounded metric function is given, under which a upper bound of metric function is defined as well.
对于一个同胚映射，本文给出了度量函数的定义，并且给出了度量函数有界的一个充分条件及在此充分条件下度量函数的一个上界。
2·Homeomorphic morphism and homotopy equivalence are two important concepts in the theory of algebraic topology.
同胚映射和同伦等价是代数拓扑学中的两个重要概念。
3·In the third chapter, we study mainly iterative roots of piecewise homeomorphic maps of an Y-star.
在第三章，我们主要研究了Y星上逐片同胚映射的迭代根的问题。