拓扑完备空间

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

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。

Its main goal is to explore information relating to the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other important problems such as the Novikov conjecture, the Baum-Connes conjucture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature and so on.

其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）大尺度几何结构的信息，建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Baum-Connes猜测， Gromov-Lawson-Rosenberg正标量曲率猜测等。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

Spatial query language ; topological relationship ; complex spatial feature ; completeness ; exclusiveness

空间查询语言；拓扑关系；复杂空间对象；完备性；互斥性

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。