实数系统的一种推广

Soeparna Darmawijaya
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引用次数: 0

摘要

本文是本人对某些代数结构的晶格拓扑研究成果的一部分;例如Rn(所有实数的n元组的集合),S (R)(所有实数序列的集合),C[a, b] ([a, b]上所有连续函数的集合),M[a, b] ([a, b]上所有可测函数的集合)。它们中的每一个都是一个晶格拓扑代数(见[6]),它们中的每一个都可以被认为是实数系统的一个推广。本文是本人对某些代数结构的晶格拓扑研究成果的一部分;例如Rn(所有实数的n元组的集合),S (R)(所有实数序列的集合),C[a, b] ([a, b]上所有连续函数的集合),M[a, b] ([a, b]上所有可测函数的集合)。它们中的每一个都是一个晶格拓扑代数(见[6]),它们中的每一个都可以被认为是实数系统的一个推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A generalization of the system of real numbers
This paper is a part of the results of my study on lattice topology on some algebraic structures; for examples on Rn (the collection of all n-tuples of real numbers), S (R) (the collection of all sequences of real numbers), C[a, b] (the collection of all continuous functions on [a, b]), and M[a, b] (the collection of all measurable functions on [a, b]). Each of them is a lattice topological algebra (See [6]) and each of them can be considered as a generalization of the system of real numbers.This paper is a part of the results of my study on lattice topology on some algebraic structures; for examples on Rn (the collection of all n-tuples of real numbers), S (R) (the collection of all sequences of real numbers), C[a, b] (the collection of all continuous functions on [a, b]), and M[a, b] (the collection of all measurable functions on [a, b]). Each of them is a lattice topological algebra (See [6]) and each of them can be considered as a generalization of the system of real numbers.
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