度量空间

In the third section,we study the relationship between the APOTP for continuous map / on a compact metric space X and that for the lift map / of / on a covering space X and show that has the APOTP if and only if has the APOTP.

在第四节中，我们研究逆极限空间上移位映射的APOTP，讨论紧致度量空间上连续映射APOTP与逆极限空间上移位映射APOTP间的关系。

The author proves theorem on contracting maps for halfmetric space and the existance of solution and the Continuousness of integral operator integral equation in Orlica space.

证明了半度量空间中的压缩映像原理，并应用其证明了Orlica空间中一类积分方程解的存在性及积分算子的连续性。

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。

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。

Similarly, a countable product of metric spaces can be obtained using the following metric

类似的，度量空间的可数乘积可以用如下度量获得

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。

We introduce a set of real functions H, and use to it to give a fixed point theorem of tother type for complex mappings on complete metric spaces, which improves and generalizes the corresponding results on compact metric spaces or under the condition of weakening compactness obtained by Fisher, Telci and Xu Xiao-li, respectively.

利用引入的实函数类H，在完备度量空间上给出了复合映射的另一种类型的不动点定理，改进并推广了Fisher、Telci和徐晓立等在紧致度量空间上或在弱化紧性条件下得到的相应结果。

At last, the similar metric p' is given on MV unit interval, and it's proved that p' is the usual metric.

最后，在MV单位区间上引入了类似p的一个度量p'，并证明了([0， 1]， p')是通常度量空间。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。