紧性

The text applies the covering theory to the study and discussion of the relative compact, the relative countably compact and the relative Lindelff compact.

运用覆盖理论，对相对紧、相对可数紧和相对Lindelff紧进行研究和讨论，给出了它们之间的一些关系，并且结合相对分离性，获得某些传递等性质。

Finally,as to an equicontinuous homeomorphism on a compact metric space,...

最后，针对紧致度量空间上的等度连续同胚，利用空间的极小性和紧致性，得到以空间中某有限个点的有限长轨道为中心，以ε2为半径的开邻域构成的有限子覆盖，并利用f的等度连续性，由该子覆盖构造出以空间任一点的有限长轨道为中心的开邻域所作成的有限子覆盖，进而得到所要结论。

Secondly,by reduction to absurdity and the sequentially compactness of the space,the minimality of a homeomorphism on a sequentially compact space is discussed.

其次，利用反证法结合空间的序列紧致性对序列紧致空间上的同胚映射的极小性进行讨论。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simon\'s nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simons nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Inspired by these results, in this paper, we first give the definition of a new mapping ? uniformly Lipschitz asymptotically nonexpansive mapping on a compact subset of a uniform convex Banach space, then construct three-step iterative sequences of uniformly Lipschitz asymptotically nonexpansive mapping in this subset . We proved the convergence of this three-step iterative sequences for uniformly Lipschitz asymptoticallynonexpansive mapping, Further more, we proved this three-step iterative sequences with an error member converge to fixed points.

从中得到启发，在本文我们首先定义了一致凸Banach空间某非空紧子集上的一种新的映射——一致李普希兹渐进非扩张映射，在该紧子集上构造关于一致李普希兹渐进非扩张映射的三步迭代序列以及具误差的三步迭代序列，先来讨论三步迭代序列的收敛性，进而讨论具误差的三步迭代序列的收敛性。

In this paper, the concepts of twelve countable compactness in symmetric topological molecular lattices are introduced.

在对称拓扑分子格中引入12种可数紧性的概念，着重指出了它们在极不连通的对称拓扑分子格中的内在联系。

In the project, we found a method for designing a family of 4-optimal double loop networks, established some sharp upper bounds of forwarding indices, distance domination nember, the edge-connectivity and the sharp upper bounds of wide-diameter and fault-tolerant diameter of Cartesian product graphs, the lower bounds of restricted edge-connectivity of digraphs and a sufficient and necessary condition for the restricted edge-connectivity of a graph to be equal to the restricted connectivity of its line graphs; raveled pancyclicity and panconnectivity and obtained the exact values of the mentioned parameters for some well-known networks.

本项目给出最优双环网络的设计方法，找到4紧优双环网络无限族，建立了路由转发指数紧的界，确定了笛卡尔乘积图的边连通度的表达式，宽直径和容错直径紧的上界，给出有向图限制边连通度的下界和无向图的限制边连通度等于它的线图限制点连通度的充要条件，对一些著名的网络确定了上述参数的精确值，讨论了宽直径和容错直径之间的关系，解决了超立方体某些变型网络的泛圈性和泛连通性，得到距离控制数的紧的上界。

By using the cone theory and the coupling upper and lower solution method, it is studied the existence uniqueness of solutions of nonlinear binary operator equations without monotone and continuity and compactness conditionsin Banach spaces.

利用锥和耦合上下解方法，研究Banach空间不具有单调性、连续性和紧性条件的非线性二元算子方程解的存在唯一性，并给出了迭代序列收敛於解的误差估计，所得结果改进和推广了混合单调算子方程的某些已知相应结果。

By using the cone theory and the coupling upper and lower solution method,it is studied the existence uniqueness of solutions of nonlinear binary operator equations without monotone and continuity and compactness conditionsin Banach spaces.

利用锥和耦合上下解方法，研究Banach空间不具有单调性、连续性和紧性条件的非线性二元算子方程解的存在唯一性，并给出了迭代序列收敛于解的误差估计，所得结果改进和推广了混合单调算子方程的某些已知相应结果。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。