同胚

According to the theorem Euler characteristic is equal to 2 on the sphere, it is show that this maps has at least one fixed point,that is to say the vector field has at least one singular point.

在地壳的每一点，由于受力定义了整个地壳上的向量场，然后利用同胚，将其转化为球面上的自映射，并根据球面的欧拉示性数等于2，说明该自映射至少有一个不动点，即向量场至少有一个奇点。

In chapter 3,we prove that a complete noncompact n-dimensional Riemannian manifold M whose Ricci curvature Ric_M ≥(n- 1) has finite topological type or diffeomorphic to R~n if its Excess function has some upper bound at a point.

第三章，我们证明了对于Ricci曲率Ric_M≥-(n-1)的完备非紧n维Riemann流形M，若它的共轭半径有正的下界且共轭半径的某个函数为M在某一点的Excess的上界时，它就有有限拓扑型或者微分同胚于n维欧几里德空间。

It is clear that for any graph G the space R and R are homeomorphic.

显然，对任意一个图G，空间 R和空间 R是同胚的。

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。

We give a sufficient condition for the self-similar set in the plane which is homeomorphic to the unit disk.

最后一章讨论自相似集的拓扑结构，给出了平面上的自相似集同胚于单位圆盘的充分条件。

In this paper, we discussed mainly the iterative roots of piecewise homeomorphic maps of an Y- star.

本文主要讨论Y星上逐片同胚映射的迭代根。

In the second chapter,we introduce some lemmas and concepts about iterative roots of piecewise homeomorphic maps of y-stars.

在第二章，我们介绍了与Y星上逐片同胚映射的迭代根有关的概念和引理。

Only if f,φ, g,φ have special structures, the proper homeomorphic function can map the solution of the system onto that of the system.

、φ(t， y具有特殊结构时，通过构造适当的同胚函数，把系统的解映射为系统解。

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。"

If the dynamicmapping thus determined is continuous,the two topological spaces is said to be homeomorphic and their respective energy shellsdo have the same dynamic property of being subdividable into invariant subspaces according to the same set of quantum num-bers.

如果这样决定的动力学映射是连续的，它就是两个拓扑空间之间的同胚映射，而两个系统的能量壳有同样的动力学性质，即可以按同一套量子数划分不变子空间。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。