查询词典 metric space

In this paper,the nonstandard analysis theory is used for inducing a metric space by a Loeb measure space.On this basis,a metric space is induced by a internal finitely additive measure space.The close relationship between the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space is illustrated with the concepts and some properties of Loeb measure.Then,some properties of the metric space that induced by a internal finitely additive measure space are studied.In the first two chapters,we first Succinctly present the origin,development and research states of the nonstandard analysis.Then,the theoretical foundation of nonstandard analysis as well as the axiomatic nonstandard analysis are given.Finally, the nonstandard model and the saturation model are discussed,as well as some natures of the nonstandard model and several equivalent conditions of saturation model are given.

本文利用非标准分析理论，在由Loeb测度空间导出度量空间的基础上，由内有限可加测度空间导出了度量空间，并借助Loeb测度的概念和若干性质证明了由标准的测度空间导出的度量空问和由内有限可加测度这个非标准的测度空间导出的度量空间有着密切的关系，在此关系的基础上还研究了由有限可加测度这个非标准的测度空间导出的度量空间的性质在第一、第二章里，我们首先简单介绍了非标准分析的产生、发展及研究现状，接着给出了非标准分析的理论基础以及公理化的非标准分析，进而讨论了非标准模型和饱和模型，并给出了非标准模型的一些性质和饱和模型的若干等价条件。

That is, any function from a discrete metric space to another bounded metric space is Lipschitz continuous, and any function from a discrete metric space to another metric space bounded by 1 is short.

就是说，从离散度量空间到另一个有界度量空间的函数是李普希茨连续的，而任何从离散度量空间到另一个有界于 1 的度量空间的函数是短映射。

The concept of G unit interval and the definition of separable degree between elements on G unit interval are given, and some properties are discussed. Based on this concept, it determined a metric p, and ([0, 1], p) becomes a metric space (It is called G unit logical metric space). In this paper, the properties and structure of G unit logical metric space are discussed in detail, and get some good results.

给出了G单位区间[0， 1]的定义并在其上引入了元素间的可分度的概念，讨论了其基本性质，并在此定义的基础上确定了一个度量P，从而([0， 1]， p)成为一个度量空间（文中称"G单位逻辑度量空间"），并对G单位逻辑度量空间的性质及其结构进行了详尽的讨论，并得到一些好的结果。

In chapter 5,we introduce the De Morgan algebra of metric and investigate the pseudo-metric Uniformity and the pseudo-metric topology and the separation axioms in De Morganalgebra of metric.We establish the Baire category theorem and the Banach contraction theo-rem,the Edelstein contraction theorem and other fixed quasi-atom theorems in De Morganalgebra of metric.In final,we give a sufficient condition for the metrization of a De Morganalgebra of topology.

在第五章里，我们地德摩根代数中引进了伪度量，探讨了伪度量一致和伪度量拓扑以及德摩根度量代数的分离公理，得到了Baire范畴定理、Banach收缩定理、Edelstein收缩定理以及其它不动拟原子定理，最后给出一个德摩根拓扑代数可度量化的充分条件。

We introduce the notion of fuzzy-valued continuous function on a compact set K in a metric space, and discuss its properties; On this base, we study the uniformly d∞-convergence of a sequence of fuzzy-valued continuous function on K. We prove that the space of fuzzy-valued continuous functions on K, i.e. C(K, E1), is a complete metric space with respect to the metric D.

引入了定义在某度量空间的紧子集K上的模糊数值连续函数和水平连续函数的概念，讨论了它们的某些性质；在此基础上，研究了K上模糊数值连续函数列的一致d∞-收敛性，证明了K上模糊数值连续函数空间C(K， E1)关于度量 D 构成一个完备的度量空间。

For example, U-space is uniformly regular and which makes it has fixed point property, U-space is uniformly non-square and thus super-reflexive, uniformly convex space and uniformly smooth space are U-spaces, and an Banach space is an U-space iff its dual space is U-space, etc. In1990s, a lot of work had been done on U-space theory, e.g., Tingfu Wang and Donghai Ji introduced the concepts of pre U-property and nearly U-property. Under the structure of Orlicz space, they made systematic investigation of these properties, and gave the criteria for an Orlicz space to have U-property.

U-空间具有一致正规结构进而具有不动点性质；U-空间是一致非方的，进而也是超自反的；一致凸空间和一致光滑空间是U-空间；Banach 空间为U-空间的充要条件是其对偶空间为U-空间，等等。20世纪90年代，国内外学者对U-空间理论做了很多工作，王廷辅，计东海等人先后引入了准U-性质与似U-性质的概念，并在Orlicz空间框架下对有关性质进行了系统研究，完整给出了Orlicz空间具有各种U-性质的判据。

By describing Pythagorean theorem, the first time-space view explain the plane-line thought which impacts human's thinking manner; the second time-space view is absolute time-space theory of Newton and three-dimensions space-time view intersected by space-time; the third space-time view is curve space-time view which is generated from Einsteinian relative theory. The fourth space-time view is the directional, irreversible entropy time-space thought; the fifth time-space view is dense time-space view of cracked fractal generated from chaos-fractal theory.

第一时空观是通过对勾股定理的描述来说明影响人们思维方式的平直时空观；第二时空观是牛顿的绝对时空理论，是时空分割的立体三维时空观；第三时空观是爱因斯坦的相对论理论所带来的弯曲时空观；第四时空观是具有方向不可逆的熵时空观；第五时空观是混沌与分形理论所带来的破碎分形的稠时空观。

Three counter-examples of topological space are proposed in this study: There are two metric spaces, X and Y, in which and are isometric, whileand are not isometric; Non-metric tight regular space is a counter-example of the separation of topological space; No non-zero continuous linear functionals of the linear topological space is a counter-example of linear topological space.

这里给出三个反例，存在两个度量空间X与Y，使X^2与Y^2等距而X与Y并不等距是拓扑空间中的反例；存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例；不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例。

Regarding (6) type, when tradition Time variable t is two spatial vectors (+ psi 1i) and (- psi 2j) Crossed products v also is not 0, it (x1, x2, x3) differs 90 compared to on speed with the three-dimensional space in the space by the pure imaginary number attribute, I=e^I pi, therefore it Number space has in the physical property with the dot product constitution the difference, because Crossed products psi 1i (X psi 2j extremely small visible it is equal to zero under the conventional speed, but is very big in the object movement speed time, Crossed products psi 1i (X psi 2j in the physical quantity and for the quantum mechanics in may not to the easy quantity, its space and the conventional space is different, the performance is intrinsic or the interior space If the definition vector (+ psi 1i) and (- psi 2j) the dot product constitutes the three-dimensional space (x1, x2, x3) is exterior space, but the three-dimensional space which (+ psi 1i) and (- psi 2j) Crossed products constitutes by the vector is the internal space, contrasts its component

对于⑥式，传统时间量t为两个空间矢量(+ψ1i)与(-ψ2j)的叉积比上速度v且不为0，其与三维空间(x1，x2，x3)在空间上相差90度以纯虚数表征，I=e^Iπ，故其与点积构成的实空间有物理性质上的不同，因为在常规速率下叉积ψ1i(Xψ2j非常小可视其等于零，而在物体运动速率很大时，叉积ψ1i(Xψ2j之中物理量与则为量子力学中的不可对易量，其空间与常规空间不同，表现为一个内在或内部性空间。若定义矢量(+ψ1i)与(-ψ2j)点积所构成的三维空间(x1，x2，x3)为外部空间，而由矢量(+ψ1i)与(-ψ2j)叉积而构成的三维空间为内部空间，对比其分量

POTS AND PANS PARTY" POTS AND PANS, LONG" POTS AND PANS, SHORT" METAL RUMMAGE WITH GRIND" METAL RUMMAGE WITH HORN" METAL RUMMAGE" METAL CRASH" METAL CRASH""CARTOON,ACCENT FADUNK" BONKS, HORN, GONG" BONKS, HORN" FUNNY BONKS AND GONG" CRASHES, FUNNY HORN, RATTLE" CLANK, CRASH, BONG, HORN" HORN, CLANK, CRASH, BONG" HORN, CLANG" BONK, BELL RATTLE, BONG" BONG, HORN, SQUAWK, CRASH" BONG, HORN, SQUAWK" SMACK AND ZING""CARTOON,ACCENT WHISTLE, CRASH, CRASH, BONG""CARTOON,ACCENT WHISTLE, CLANK, CRASH, BONG""CARTOON,ACCENT WHISTLE, CLANK, CRASH, BONK""CARTOON,ACCENT BONK, WHIRL, HORN""CARTOON,ACCENT BONK AND WHIRL""CARTOON,ACCENT CLANK AND GRIND""CARTOON,ACCENT CLANK AND WHIRL""CARTOON,ACCENT SIREN WHISTLE, BRAKE HIT, CLANK""CARTOON,ACCENT SHORT SIREN WHISTLE, BRAKE DRUM HIT""CARTOON,ACCENT SHORT SIREN WHISTLE, BRAKE DRUM HIT""CARTOON,ACCENT SIREN WHISTLE, BRAKE DRUM HIT""CARTOON,ACCENT FUNNY SLIDE DOWN WITH BELL RATTLE""CARTOON,ACCENT FUNNY SLIDE UP WITH BELL RATTLE""CARTOON,ACCENT SLIDE DOWN, BELL""CARTOON,ACCENT SLIDE DOWN, BOING, CRASH""CARTOON,ACCENT SLIDE DOWN, BOING, CRASH""CARTOON,ACCENT SLIDE DOWN, BOING""CARTOON,FISH BUCKET OF FISH DROPPING ON PIER""CARTOON,CLOCK CLOCK TICKING""CARTOON,CLOCK CLOCK TICKING""CARTOON,ACCENT DESCENDING WARBLE GLISS""CARTOON,ACCENT ASCENDING WARBLE GLISS""CARTOON,ACCENT DESCENDING BONK GLISS""CARTOON,ACCENT ASCENDING BONK GLISS""CARTOON,ACCENT DESCENDING ZIP GLISS""CARTOON,ACCENT ASCENDING ZIP GLISS""CARTOON,ACCENT DESCENDING ZIP GLISS""CARTOON,ACCENT ASCENDING ZIP GLISS""CARTOON,ACCENT SPIT IN A BUCKET""CARTOON,ACCENT SPIT IN A BUCKET""CARTOON,ACCENT BOING""CARTOON,ACCENT FLAPPING BONKS""CARTOON,ACCENT IMPACT, WARBLE, BING""CARTOON,ACCENT IMPACT, SPLAT""CARTOON,ACCENT SHORT FALL WHISTLE, SMALL DING""CARTOON,ACCENT SHORT FALL WHISTLE, SPLAT""CARTOON,ACCENT ZIP, SMALL DING""CARTOON,ACCENT ZIP, HORN, WARBLE""CARTOON,ACCENT ZIP, RAZZ""CARTOON,ACCENT ZING, ZING""CARTOON,ACCENT BONKS, POPS, HORN""CARTOON,ACCENT BONKS, POPS""CARTOON,ACCENT BONKS, ZIP""CARTOON,ACCENT BONKS, RAZZ, TWANG""CARTOON,ACCENT BONG, POPS, BOING""CARTOON,ACCENT BONK, POPS, BING""CARTOON,ACCENT ZIP, BONKS, POPS""CARTOON,ACCENT WHIZ, POPS, HORN""CARTOON,ACCENT WHIZ, BONKS" SPACE LARGE SPACE COMPUTER SPACE ENERGY HUM SPACE LANDING SPACE LANDING SPACE SPACE PASS BY SPACE LIFTOFF SPACE LIFTOFF "SPACE,ZAP POWER ZAP

坛坛罐罐党"锅碗瓢盆龙"锅碗瓢盆，淡"金属带磨翻找"金属翻找，喇叭"金属翻找"金属崩溃"金属崩溃""卡通，口音FADUNK" BONKS，角，宫" BONKS，喇叭"滑稽BONKS和宫"崩溃，滑稽的号角，摇铃"叮当，碰撞，邦格，喇叭"喇叭，叮当，碰撞，奉："角，铛"邦克，钟摇铃，奉"峰，角，发牢骚，崩溃"邦，喇叭，发牢骚"嫌和Zing""卡通，口音哨子，崩溃，崩溃，奉""卡通，口音哨子，叮当，碰撞，奉""卡通，口音哨子，叮当，碰撞，邦克""卡通，重音邦克，旋转，圆号""卡通，口音邦克和漩涡""卡通，口音叮当和研磨""卡通，口音叮当和漩涡""卡通，口音警笛哨子，制动冲击，叮当""卡通，口音短警笛哨子，制动鼓打""卡通，口音短警笛哨子，制动鼓打""卡通，口音警报器哨子，制动鼓打""卡通，口音滑稽滑下贝尔摇铃""卡通，口音滑稽幻灯片与贝尔向上摇铃""卡通，口音滑下，钟""卡通，口音下滑，博英，崩溃""卡通，口音下滑，博英，崩溃""卡通，口音下滑，博英""动漫，鱼鱼斗安码头不用""卡通，时钟滴答作响的时钟""卡通，时钟滴答作响的时钟""卡通，口音降沃布尔GLISS""卡通，口音递增沃布尔GLISS""卡通，口音降邦克GLISS""卡通，口音递增邦克GLISS""卡通，口音降邮编GLISS""卡通，口音递增邮编GLISS""卡通，口音降邮编GLISS""卡通，口音递增邮编GLISS""卡通，在斗森垃圾""卡通，在斗森垃圾""卡通，口音博英""卡通，口音拍打BONKS""卡通，口音的影响，沃布尔，邴""卡通，口音的影响，图示""卡通，口音短秋季哨子，小鼎""卡通，口音短秋季哨子图示"："卡通，口音邮编，小鼎""卡通，口音邮编，喇叭，沃布尔""卡通，口音邮编，非难""卡通，口音ZING中，ZING中""卡通，口音BONKS，持久性有机污染物，喇叭""卡通，口音BONKS，持久性有机污染物""卡通，口音BONKS，邮编""卡通，口音BONKS，非难，鼻音""卡通，口音邦，持久性有机污染物，博英""卡通，口音邦克，持久性有机污染物，邴""卡通，口音邮编，BONKS，持久性有机污染物""卡通，口音奇才，持久性有机污染物，喇叭""卡通，口音能手，BONKS"计算机空间大空间宇宙能源本田空间着陆空间着陆经过空间空间空间发射空间发射空间"，ZAP公司电力ZAP公司

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。