Kuratowski Monoids on Posets
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911232659816448 |
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| author | Bowron, Mark |
| author_facet | Bowron, Mark |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kuratowski Monoids on Posets Bowron, Mark General Topology 06F05 (Primary) 06A15, 06D22, 54A05 (Secondary) 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. |
| title | Kuratowski Monoids on Posets |
| topic | General Topology 06F05 (Primary) 06A15, 06D22, 54A05 (Secondary) |
| url | https://arxiv.org/abs/2504.14475 |