{"title":"极限和连续性","authors":"Walter Noll","doi":"10.4135/9781544307770.n2","DOIUrl":null,"url":null,"abstract":"(ξa)i := ξai for all ξ ∈ R and i ∈ I. (1.2) We are here interested in the case when I := N× or I := N, in which case the elements of R are called real sequences. We deal explicitly only with the case I := N×, but all the definitions and results below apply also to the case I := N. Definition 1: We say that the sequence b ∈ RN is a subsequence of a given sequence a ∈ RN if b = a ◦ σ for some strictly isotone σ : N× → N×, so that","PeriodicalId":377607,"journal":{"name":"Analysis and Beyond","volume":"112 50","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Limits and continuity\",\"authors\":\"Walter Noll\",\"doi\":\"10.4135/9781544307770.n2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"(ξa)i := ξai for all ξ ∈ R and i ∈ I. (1.2) We are here interested in the case when I := N× or I := N, in which case the elements of R are called real sequences. We deal explicitly only with the case I := N×, but all the definitions and results below apply also to the case I := N. Definition 1: We say that the sequence b ∈ RN is a subsequence of a given sequence a ∈ RN if b = a ◦ σ for some strictly isotone σ : N× → N×, so that\",\"PeriodicalId\":377607,\"journal\":{\"name\":\"Analysis and Beyond\",\"volume\":\"112 50\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-04-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis and Beyond\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4135/9781544307770.n2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Beyond","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4135/9781544307770.n2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
(ξa)i := ξai for all ξ ∈ R and i ∈ I. (1.2) 我们在此关注的是 I := N× 或 I := N 的情况，在这种情况下，R 的元素称为实数序列。我们只明确处理 I := N× 的情况，但下面的所有定义和结果也适用于 I := N 的情况。 定义 1：如果 b = a ◦ σ 为某个严格同调的 σ : N× → N×，则我们说序列 b∈ RN 是给定序列 a∈ RN 的子序列，从而
(ξa)i := ξai for all ξ ∈ R and i ∈ I. (1.2) We are here interested in the case when I := N× or I := N, in which case the elements of R are called real sequences. We deal explicitly only with the case I := N×, but all the definitions and results below apply also to the case I := N. Definition 1: We say that the sequence b ∈ RN is a subsequence of a given sequence a ∈ RN if b = a ◦ σ for some strictly isotone σ : N× → N×, so that
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
