Kuratowski Monoids on Posets

Abstract

Recent results of Ciraulo are used to prove that operators $c$, $i$ on an arbitrary poset subject to the usual general closure and interior axioms -- but not subject to the usual duality, for there is no complement -- always generate one of $18$ different monoids under composition. We also show that there are no missing edges in a certain Hasse diagram conjectured by Ciraulo to represent the interior-pseudocomplement monoid on an arbitrary poset.

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