度量空间

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)。

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。

We show that there are 'many' compacta admitting completely scrambled homeomorphisms, which include some countable compacta, the cantor set and continua of arbitrary dimension.

并说明了"许多"紧度量空间其上存在完全混沌的系统，这些空间包括一些可数的紧度量空间、康托集和任意维的连续统。

It is shown there are"many"compacta admitting compeletly chaotic systems, which include some countable compacta, the cantor set and continua of arbitrary dimension.

构造了"许多"紧度量空间其上存在完全混沌的系统，这些空间包括一些可数的紧度量空间、康托集和任意维的连续统。

"Two- and three-dimensional Euclidean spaces are metric spaces, as are inner product spaces, vector spaces, and certain topological spaces."

二维和三维的欧几里德空间是度量空间。另外，内乘空间、向量空间以及某些拓扑空间等也都是度量空间

Using the soliton theory we obtain a method to contract isometric immersions from indefinite space forms into indefinite space forms with the same index.

我们利用孤立子理论得到了构造有相同指标的不定度量空间型到不定度量空间型的等距浸入的方法。

Using the soliton theory we obtain a method to contruct isometric immersions fromindefinite space forms into indefinite space forms with the same index.

靳红 ，陈维桓我们利用孤立子理论得到了构造有相同指标的不定度量空间型到不定度量空间型的等距浸入的方法。

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。

In chapter one, the background and current situation of the nonlinear operator theory in probabilistic metric spaces are introduced, and the preliminaries of probabilistic metric spaces are given. The main problems studied in the thesis, the expected conclusions and the study and research significance of this thesis are introduced.

第一章，介绍了概率度量空间中非线性算子理论发展的历史背景、现状以及概率度量空间中的预备知识；介绍了本文所研究的主要问题、预期取得的结果以及研究意义。

We also obtain a new judgement theorem for hereditarily metaLindelof space and paracompact space. In addition, we give a depiction for g-metrizable space from a new direction with σ—ωHCP closed weak base.

f空间和仿紧空间的判定方法，并给出了g-可度量空间关于σ-弱遗传闭包保持闭弱基的一个刻画，进一步丰富和发展了广义度量空间的基本理论。

I smile at your play with that little bit of a broken twig.

我微笑着看你玩那一段小小的树枝。

They may be produced for almost any shaft angle.

他们可能在制作中几乎任何一个轴角。