查询词典 metric space

In the fourth chapter,first of all,a metric space is derived by the Loeb measure space which is a standard measure space,follow that the Completeness,separability and the Baire theorem are expressed.

第四章中，首先由Loeb测度这个标准测度空间导出度量空间，接着讨论了该度量空间的完备性和可分性以及其Baire定理(来源：A8525B52C论文网www.abclunwen.com)。

It has a long history to study on the problem of best restricted range approximationin a space of real-valued continuous functions on a closed interval, while the corresponding problem in a space of complex-valued continuous functions on a compact metric space was just introduced in recent years.

三。实值连续函数空间中最佳限制值域逼近问题的研究有较长历史，而复值连续函数空间中相应问题的研究却是近几年来的事情。

This method bases on distance transformation in Euclidean metric with the computational complexity of O(2+kn,and is the same with non-Euclidean metric space.

基于欧氏空间中离散点集的2阶V图距离变换原理，论述了栅格形式下离散点集和一般点集图形的2阶V图生成的方法，确定了它的时间复杂性为O(2+kn，适用于欧氏及非欧度量空间的自然图形2阶V图构造。

Topological space, metric space, normed linear space and inner product space

在直角空间内建立了主从运动映射模型。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

The nonstandard anslysis theory is used in the κ-saturated nonstandard model, the definition of the quasi-near-standard points in a metric space is given and it is proved that a point in nonstandard metric space is quasi-near-standard point if and only if its monad contained in every *-open ball of some standard point.

在κ-饱和的非标准模型下，采用非标准分析方法，提出了度量空间中的拟近标准点的定义，得到了非标准度量空间中的点是拟近标准点的充要条件是它属于某一个标准点的每一个*-开球，证明了度量空间的非标准完备化恰是该空间的非标准扩张中拟近标准点集的商空间。

Each kind of theory and technology about health safeguard can be integrated into a grading describable system. The 5 kinds basic space, which is derived sequentially from topological space, regular space, metric space, measured space and continuous space, are the mathematical base to structure the method of health safeguard.

从泛函分析的角度全面总结了各种健康保障理论与技术，将其统一到一个递级的描述系统中，由拓扑空间、规则空间、度量空间、测度空间和连续空间逐步继承而来的5类基本空间是构造健康保障方法的数学基础。

Since the commonly-used parameter analysis method is liable to cause the diversity of results in style investment analysis, the method of subdominant ultra-metric space is introduced to the study of style investment. Subdominant ultra-metric space is provided with the exactly defined topology sequence, and corresponded with index hierarchical structure and style.

针对常用的参数分析方法在证券风格投资分析中容易导致结果的差异性问题，提出将亚超度量空间方法引入到风格投资研究中，因为具有准确定义拓扑序列的亚超度量空间与指数分层结构、风格能够一一对应。

Firstly, the distance between stocks are calculated by using prices of stocks, and subdominant ultra-metric space by associating the minimum spanning tree of portfolio. Secondly, the subdominant ultra-metric space to the chart of index hierarchical structure is transformed, and finally the distribution of style is gained. Using sample of Shanghai Stock 50 Index from 2004 to 2007, the demonstration result shows that style of industry is more prominent horizontally, especially in the bank and steel industries. The style of region and cross holding also exists. And after the reform of non-tradable shares, style of industry becomes more obvious vertically and more other styles also occur.

首先利用股票价格计算出股间距离，并采用关联该证券组合的最小生成树优化方法，从而得到亚超度量空间；其次将此亚超度量空间转换成指数分层结构树图，最后得到风格的分布特征。2004~2007年的上证50实证结果表明：横向来看以行业分类的风格较为显著，其中以银行和钢铁也最为明显，此外还有与地区差异、交叉持股相关的风格效应显现；纵向则在股改后行业风格效应更显著，其它的风格也显现得更多。

Certainly the discrete metric space is free when the morphisms are all uniformly continuous maps or all continuous maps, but this says nothing interesting about the metric

任何从离散拓扑空间到另一个拓扑空间的函数是

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。