{"title":"的连续单体","authors":"Ernie Manes","doi":"10.1016/j.entcs.2020.09.009","DOIUrl":null,"url":null,"abstract":"<div><p>Continuous monads are an axiomatic class of submonads of the double power set monad. <em>ρ</em>-sets are an axiomatic generalization of directed sets. The <em>ρ</em>-generalization of continuous lattices arises as the algebras of a continuous monad and conversely. Each <em>ρ</em>-continuous poset has two topologies which respectively generalize the Scott and Lawson topologies. Each <em>ρ</em>-contnuous lattice is compact in the canonical topology if and only if the corresponding continuous monad contains the ultrafilter monad.</p></div>","PeriodicalId":38770,"journal":{"name":"Electronic Notes in Theoretical Computer Science","volume":"352 ","pages":"Pages 173-190"},"PeriodicalIF":0.0000,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.entcs.2020.09.009","citationCount":"0","resultStr":"{\"title\":\"Continuous Monads\",\"authors\":\"Ernie Manes\",\"doi\":\"10.1016/j.entcs.2020.09.009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Continuous monads are an axiomatic class of submonads of the double power set monad. <em>ρ</em>-sets are an axiomatic generalization of directed sets. The <em>ρ</em>-generalization of continuous lattices arises as the algebras of a continuous monad and conversely. Each <em>ρ</em>-continuous poset has two topologies which respectively generalize the Scott and Lawson topologies. Each <em>ρ</em>-contnuous lattice is compact in the canonical topology if and only if the corresponding continuous monad contains the ultrafilter monad.</p></div>\",\"PeriodicalId\":38770,\"journal\":{\"name\":\"Electronic Notes in Theoretical Computer Science\",\"volume\":\"352 \",\"pages\":\"Pages 173-190\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.entcs.2020.09.009\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571066120300554\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Computer Science\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571066120300554","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Computer Science","Score":null,"Total":0}
Continuous monads are an axiomatic class of submonads of the double power set monad. ρ-sets are an axiomatic generalization of directed sets. The ρ-generalization of continuous lattices arises as the algebras of a continuous monad and conversely. Each ρ-continuous poset has two topologies which respectively generalize the Scott and Lawson topologies. Each ρ-contnuous lattice is compact in the canonical topology if and only if the corresponding continuous monad contains the ultrafilter monad.
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ENTCS is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication and the availability on the electronic media is appropriate. Organizers of conferences whose proceedings appear in ENTCS, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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