Kuratowski Monoids on Posets
General Topology
2025-10-28 v2
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.
Cite
@article{arxiv.2504.14475,
title = {Kuratowski Monoids on Posets},
author = {Mark Bowron},
journal= {arXiv preprint arXiv:2504.14475},
year = {2025}
}
Comments
16 pages, 7 figures