英语语法分析

As mathematicians say, “Every simply connected closed 3-manifold is homeomorphic to a 3-sphere.”

用数学语言表达就是“每个单连通3重（3-manifold）封闭体与一个三维球体同胚（homeomorphic）。”

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。

In this paper, some results on fixed points of homeomorphic maps in metric Spaces have been obtained.

本文给出了度量空间中某些同胚非扩张映射不动点存在的充分必要条件。