{"title":"具有非闭偏序的可度量半拓扑半格","authors":"T. Banakh, S. Bardyla, A. Ravsky","doi":"10.1515/taa-2020-0006","DOIUrl":null,"url":null,"abstract":"Abstract We construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice, having a prescribed countable family of convergent sequences.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"8 1","pages":"67 - 75"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2020-0006","citationCount":"5","resultStr":"{\"title\":\"A metrizable semitopological semilattice with non-closed partial order\",\"authors\":\"T. Banakh, S. Bardyla, A. Ravsky\",\"doi\":\"10.1515/taa-2020-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice, having a prescribed countable family of convergent sequences.\",\"PeriodicalId\":30611,\"journal\":{\"name\":\"Topological Algebra and its Applications\",\"volume\":\"8 1\",\"pages\":\"67 - 75\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/taa-2020-0006\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topological Algebra and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/taa-2020-0006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Algebra and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/taa-2020-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
A metrizable semitopological semilattice with non-closed partial order
Abstract We construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice, having a prescribed countable family of convergent sequences.