{"title":"实数系统的一种推广","authors":"Soeparna Darmawijaya","doi":"10.1063/1.5139119","DOIUrl":null,"url":null,"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.","PeriodicalId":209108,"journal":{"name":"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","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A generalization of the system of real numbers\",\"authors\":\"Soeparna Darmawijaya\",\"doi\":\"10.1063/1.5139119\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":209108,\"journal\":{\"name\":\"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\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"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\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/1.5139119\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"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","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.5139119","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.