{"title":"Structure of homogeneous chains","authors":"T. Ohkuma","doi":"10.2996/kmj/1138843293","DOIUrl":null,"url":null,"abstract":"Especially, for any pair of elements a, b of X, the set of elements between (properly) a and b is an interval of X, which we ca31 an open interval (a, b). The set oϊ upper bounds and the set of lower bounds of an element a of X, excluding the element a, are also called (unbounded) open intervals, and are denoted by (a,-) and (-, a) respectively. When two elements a and b are adjoined to the open interval (a, bj, we call it a closed interval [a, bl [a, b) denotes the interval (a, b)with adjoined a only, (a, b], [a, ) , and (-, a] are similarly defined*,","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Seminar Reports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2996/kmj/1138843293","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Especially, for any pair of elements a, b of X, the set of elements between (properly) a and b is an interval of X, which we ca31 an open interval (a, b). The set oϊ upper bounds and the set of lower bounds of an element a of X, excluding the element a, are also called (unbounded) open intervals, and are denoted by (a,-) and (-, a) respectively. When two elements a and b are adjoined to the open interval (a, bj, we call it a closed interval [a, bl [a, b) denotes the interval (a, b)with adjoined a only, (a, b], [a, ) , and (-, a] are similarly defined*,
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