{"title":"Does the endomorphism poset $P^P$ determine whether a finite poset $P$ is connected?\u0000 \u0000An issue Duffus raised in 1978","authors":"J. Farley","doi":"10.21136/mb.2022.0010-22","DOIUrl":"https://doi.org/10.21136/mb.2022.0010-22","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":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41537603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}