{"title":"On the algebraic dimension of Riesz spaces","authors":"N. Baziv, O. B. Hrybel","doi":"10.30970/ms.56.1.67-71","DOIUrl":null,"url":null,"abstract":"We prove that the algebraic dimension of an infinite dimensional $C$-$\\sigma$-complete Riesz space (in particular, of a Dedekind $\\sigma$-complete and a laterally $\\sigma$-complete Riesz space) with the principal projection property which either has a weak order unit or is not purely atomic, is at least continuum. A similar (incomparable to ours) result for complete metric linear spaces is well known.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematychni Studii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/ms.56.1.67-71","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We prove that the algebraic dimension of an infinite dimensional $C$-$\sigma$-complete Riesz space (in particular, of a Dedekind $\sigma$-complete and a laterally $\sigma$-complete Riesz space) with the principal projection property which either has a weak order unit or is not purely atomic, is at least continuum. A similar (incomparable to ours) result for complete metric linear spaces is well known.