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Keywords:
(partially) ordered set; exponentiation; connected
(partially) ordered set; exponentiation; connected
Summary:
Duffus wrote in his 1978 Ph.D. thesis, ``It is not obvious that $P$ is connected and $P^P\cong Q^Q$ imply that $Q$ is connected'', where $P$ and $Q$ are finite nonempty posets. We show that, indeed, under these hypotheses $Q$ is connected and $P\cong Q$.
References:
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