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In 1978, Dwight Duffus---editor-in-chief of the journal "Order" from 2010 to2018 and chair of the Mathematics Department at Emory University from 1991 to2005---wrote that "it is not obvious that $P$ is connected and $P^P$ isomorphicto $Q^Q$ implies that $Q$ is connected," where $P$ and $Q$ are finite non-emptyposets. We show that, indeed, under these hypotheses $Q$ is connected and$P\cong Q$.

An Issue Raised in 1978 by a Then-Future Editor-in-Chief of the Journal  "Order": Does the Endomorphism Poset of a Finite Connected Poset Tell Us That  the Poset Is Connected?