查询词典 Hausdorff space

Firstly, we recall some notions and results about space theory, including Hausdorff space, Hausdorff distance between sets , Baires category about sets and convex set. Secondly, the semi-continuity, closure, compactness of set-valued maps are introduced in set-valued analysis. Finally, essential point, essential set and essential component are introduced.

其中，空间理论及凸集的基本知识介绍了Hausdorff空间、集合间的Hausdorff距离、集合的Baire分类、以及凸集等四个方面；集值分析部分主要介绍单值映射的半连续性以及集值映射的半连续性、闭性和紧性；本质点、本质集和本质连通区部分主要介绍了本质点、本质集和本质连通区等有关概念和性质。

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。

In Chapter One,we find the relationship between strong open set condition , Hausdorff dimension,the positivity of the Hausdorff measure and β space of graph-directed self-similar sets in complete metric spaces.

在第一章中，我们讨论了在度量空间中，图定向自相似集的强开集条件、Hausdorff维数，正的Hausdorff测度和β空间之间的关系。

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。

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

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In Chapter 1, we introduce the definitions of Hausdorff dimension and Hausdorff measure, and some related definitions and theorems.

第一章介绍Hausdorff维数和Hausdorff测度的定义及一些相关的定义和定理。

Another problem he did not answer is the Hausdorff dimension and the exact Hausdorff measure functions for level sets of this processes.

为比较起见，我们回顾了一些相关过程的水平集的Hausdorff测度函数的解决过程。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？