{"title":"Connected topological lattice-ordered groups","authors":"Francis Jordan","doi":"10.1007/s00012-022-00800-6","DOIUrl":null,"url":null,"abstract":"<div><p>We answer two open problems about lattice-ordered groups that admit a connected lattice-ordered group topology. We show that, in the general case, admitting a connected lattice-ordered group topology does not effect the algebraic structure of the lattice-ordered group. For example, admitting a connected lattice-ordered group topology does not imply that the lattice-ordered group is Archimedean or even representable. On the other hand, if one assumes that the lattice-ordered group has a basis, then admitting a lattice-ordered group topology implies that the lattice-ordered group is a subdirect product of copies of the real numbers.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-022-00800-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We answer two open problems about lattice-ordered groups that admit a connected lattice-ordered group topology. We show that, in the general case, admitting a connected lattice-ordered group topology does not effect the algebraic structure of the lattice-ordered group. For example, admitting a connected lattice-ordered group topology does not imply that the lattice-ordered group is Archimedean or even representable. On the other hand, if one assumes that the lattice-ordered group has a basis, then admitting a lattice-ordered group topology implies that the lattice-ordered group is a subdirect product of copies of the real numbers.
期刊介绍：
Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
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