{"title":"Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected?\n \nAn issue Duffus raised in 1978","authors":"J. Farley","doi":"10.21136/mb.2022.0010-22","DOIUrl":null,"url":null,"abstract":". Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that P is connected and P P ∼ = Q Q imply that Q is connected”, where P and Q are finite nonempty posets. We show that, indeed, under these hypotheses Q is connected and P ∼ = Q .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2022.0010-22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
. Duffus wrote in his 1978 Ph.D. thesis, “It is not obvious that P is connected and P P ∼ = Q Q imply that Q is connected”, where P and Q are finite nonempty posets. We show that, indeed, under these hypotheses Q is connected and P ∼ = Q .
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