查询词典 metric topology

If the production of the two particles alters the topology and metric of the space, producing a lengthening wormhole between them as they separate, for instance, then the effects from one to the other may be quite local.

如果两个粒子的生成使空间的拓扑与量度发生了改变的话，例如，若两个粒子分离时在二者之间形成了一个不断伸长的虫洞的话，那么（在这个被重新量度了的空间中看来）这两个粒子之间的作用就有可能是完全局域性的了。

With regard to the Einstein-Podolsky-Rosen paradox and Bell's inequality, when it is said that the correlation between the separated particles violates locality, it is assumed that the topology and metric of the space have stayed fixed.

就爱波罗悖论（Einstein-Podolsky-Rosen Paradox）和贝尔不等式而言，当说分离粒子之间的关联违反了局域性时，它假定了空间的拓扑与量度是不变的。

Some important properties of L-topological spaces, induced topological spaces, fuzzy real lines and fuzzy metric spaces in topology on lattices are obtained.

在格上拓扑中，对L-拓扑空间、诱导拓扑空间、fuzzy 实直线和fuzzy度量空间等的性质研究，得到了一系列重要的结果。

By dropping this assumption of fixed topology and metric, one can investigate alternative theories within differential geometry that yield an appropriately changing topological structure, and search for and check its testable consequences.

通过抛弃这一拓扑与量度确定不变的假设，在一个能生成一种适当的变化性拓扑架构的微分几何学之中，我们就可以探究其他的理论并寻找与检验其可检验的结果。

Then a bit sequence CID is determined by the interest,and CID is the main metric to organize topology—nodes with the close CID will form a community which is a dense subgraph.

在这种模型里，每个节点由自身的资源整体类型倾向决定自己的兴趣，并且采用树形结构来表达兴趣；然后节点由兴趣产生一个二进制序列的CID，CID将成为拓扑形成的主要依据--具有相近CID的节点能聚集成一个连通性较高的子图。

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。

By properties of a real function, fixed points problem on two complete metric spaces are discussed.The result generalizes corresponding result of Fisher.Moreover, this result provides a general convergence rate estimate. Meanwhile, we discuss the existence of fixed point on two normed linear spaces under the condition of weak topology, and we obtain a new fixed point theorem.

利用实函数性质，讨论了两个不同度量空间中两个映象乘积的不动点问题，推广了Fisher的主要结果，并给了出逼近不动点的敛速估计；同时，在弱拓扑的意义下，利用分析的方法，讨论了赋范空间中有关映象不动点的存在性，得到一个新的不动点定理。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。