{"title":"A metrizable Lawson semitopological semilattice with non-closed partial order","authors":"T. Banakh, S. Bardyla, A. Ravsky","doi":"10.15673/tmgc.v13i3.1756","DOIUrl":null,"url":null,"abstract":"We construct a metrizable Lawson semitopological semilattice $X$ whose partial order $\\le_X\\,=\\{(x,y)\\in X\\times X:xy=x\\}$ is not closed in $X\\times X$. This resolves a problem posed earlier by the authors.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the International Geometry Center","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15673/tmgc.v13i3.1756","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: 2
Abstract
We construct a metrizable Lawson semitopological semilattice $X$ whose partial order $\le_X\,=\{(x,y)\in X\times X:xy=x\}$ is not closed in $X\times X$. This resolves a problem posed earlier by the authors.
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