查询词典 metric space

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。

We show that the whole space IF~*(R, d_∞~* is complete metric space, and when K is a nonempty compact subset of R, the metric space IF~*(K,d~* and IF~*(K,d_p~* are complete.

我们证明了当K是R上的非空紧子集时，紧支撑包含在K中的所有区间值模糊数所成之集TG~*

E〓 is endowed with a new metric D, such that becomes a complete metric space. After that a locally convex complete pseudonormed space is constructed. Finally, E〓 is embedded into isometrically, and isomorphically.

在n维非紧模糊数空间E〓上引入一个新的度量D，使得成为一个完备的度量空间，然后我们构造了一个局部凸的完备赋准范空间，并将n维非紧模糊数空间等距同构地嵌入到空间之中。

Letbe a compact metric space, f: X→X a continuous map, and K(X,H a compact metric space consisting of all nonempty compact subsets of X.

设为紧致度量空间， f： X→X连续， K(X，H是 X所有非空紧致子集构成的紧致度量空间。

In the fifth chapter,we mainly discuss the relationship of the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space.

在第五章，我们重点讨论了由有限测度空间导出的度量空间和由内有限可加测度空间导出的度量空间的关系，然后在此关系的基础上研究了由内有限可加测度空间导出的度量空间的性质。

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。

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。

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 main purpose of this paper is to study the quasi-near-standard points in a metric space and the nonstandard completion of a metric space.

研究了度量空间中的拟近标准点和度量空间的非标准完备化。

The measurement in set theory, the properties of Metric Space, Measurement Topology, Measurable Space, Perfect Metric Space and its application in first order circuit are explored in this paper.

本文论述了集合上的度量、度量空间的性质、度量拓扑、可度量化空间、完备度量空间、及一阶电路中的度量空间。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失