Kuratowski Monoids on Posets

2025/04/20 by Mark Bowron, Bowron, Mark · 1 voice
Mathematics · #06D22 #06F05 (Primary) 06A15 #54A05 (Secondary) #FOS: Mathematics #General Topology (math.GN) #math.GN

paper · pdf · doi:10.48550/arxiv.2504.14475

arxiv published 2025/04/20 · arxiv updated 2025/10/27

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.

Citations

• A Kuratowski closure-complement variant whose solution is independent of ZF
• The closure-complement-frontier problem in saturated polytopological spaces
• The radical-annihilator monoid of a ring
• Kuratowski monoids of n-topological spaces
• Kuratowski's Theorem for Two Closure Operators
• Quotient Complexity of Closed Languages
• Closures in Formal Languages and Kuratowski's Theorem
• Variations on Kuratowski's 14-set theorem

Discussions

• Mark Bowron: Kuratowski Monoids on Posets https://arxiv.org/abs/2504.14475 https://arxiv.org/pdf/2504.14475 https://arxiv.org/html/2504.14475 [bsky, 0 points, 1 comments]

Related

• The monoid consisting of Kuratowski operations
• Kuratowski's Theorem for Two Closure Operators
• The closure-complement-frontier problem in saturated polytopological spaces
• Closures in Formal Languages and Kuratowski's Theorem
• CW posets after the Poincare Conjecture