Kuratowski Monoids on Posets
Abstract
Ciraulo recently showed that Kuratowski's closure-complement problem for arbitrary powersets of topological spaces extends constructively to the interior-pseudocomplement problem for arbitrary posets, using the closure-interior problem for posets (CIP) as a natural starting point. After a brief overview of CIP, we resolve two diagram-completeness problems left open by Ciraulo. Finally, we study operator semigroups arising from a little-known 1941 theorem of Chittenden, which generalizes CIP.
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