metric normal form of quadratic form
- metric normal form of quadratic form的基本解释
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二次形式的度量标准形式
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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。
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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。
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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。
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metric normal form of quadratic form:二次形式的度量标准形式
metric form 度量形式 | metric normal form of quadratic form 二次形式的度量标准形式 | metric space 度量空间