同胚的

It's really the natural setting for algebraic topology because the traditional algebraic invariants (fundamental group, homolog group,etc.) arc isomorphic not only for homeomorphic spaces but for spaces of the same homotopy type. Homtopy epimorphisms and monomorphisms are special morphisms in the category of topological spaces and the initial research of them may be traceable to S.T.

同伦论的本质是利用比同胚关系更广泛的等价关系—同伦关系来对拓扑空间进行研究，这也是代数拓扑研究中一种自然的考虑，因为传统的代数不变量不仅在同胚的空间之间保持同构，而且在具有相同伦型的空间之间也保持同构。

Secondly, for the boundary correspondence of affine stretch on hyperbolic regions, we prove that the above conclusion is also true. Finally, we pose a sufficient and necessary condition for the same conclusion.

最后利用退化的四边形序列，给出了拟对称同胚的极值拟共形延拓的最大伸缩商、四边形模之比的上确界及拟对称同胚的边界伸缩商三者相等的一个充要条件。

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章给出了以环面作为边界的两个3维流形在作融合积时不产生新的不可压缩曲面的一个充分必要条件，并将这个结果与关于环面到自身的自同胚类的分类的结果相结合，证明了本文的一个核心结论，即存在无穷多个互不同胚的3维流形满足除了一个环面以外不含有其他的不可压缩曲面。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

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。

It is proved that two sequences of Markov maps on the circle generated homeomorphic inverse limit spaces if each pair of the bounding maps with the same subscript are of the same Markov type with respect to a fixed arrangement of the two partitions.

证明了圆周上两个关于两组固定分点的Markov映射列在相同下标的两个约束映射总是关于两组分点的固定次序Markov同型的条件下生成同胚的逆极限空间。

In particular, we obtain a condition for which a homeomorphism is a non-wanderinghomeomorphism.

最后，我们还得到了一个同胚是非游荡同胚的判定条件。

The present paper presents the chain recurrent set with the expansive homeomorphism and shadowing properties and this connection for the mistake in literature [1] and its proof.

给出具有跟踪性可扩同胚的链回归集的几个性质，指出以往文献中证明链回归集无环性时的错误之处，并给出严格的证明。

Finally,by applying a ran-dom version of Kifer's large deviation theorem and the volume lemma,we prove thelevel-1 LDT for randomly perturbed Axiom A attractors of diffeomorphisms withrespect to the Lebesgue measure.

最后，利用Kifer的大偏差定理的随机版本和体积引理，我们证明了微分同胚的公理A吸引子的随机扰动系统相对Lebesgue测度的level-1 LDT。

The so-called AT-algebras are inductive limits of finite direct sums of matrices over the extension algeras of circle algebra by K, where K is the C~*— algebra of all compact operators on a separable infinite dimensional Hilbert space.

若V_*与V_*同构，且保持单位元等价类；T与T仿射同胚，且同构映射与同胚映射相容，则存在E与E′的同构导出上述同构和同胚，所谓AT-代数即为圆代数通过κ的本质酉扩张的矩阵代数的有限直和的归纳极限，这里κ为可分的无限维复Hilbert空间上的紧算子全体，不变量中的V*为三变元Abel半群，T为迹态空间，[1]为单位元所在的Murray-von Neumann等价类，r_E为连接映射。

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 。