A generalization of the system of real numbers

PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations Pub Date : 2019-12-19 DOI:10.1063/1.5139119

Soeparna Darmawijaya

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Abstract

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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实数系统的一种推广

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。

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PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations

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