Modal Logics for Products of Topologies
J.F.A.K. van Benthem, Guram Bezhanishvili, Balder ten Cate, Darko Sarenac · 2004
We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 S4. We axiomatize the modal logic of products of topological spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers Q Q with the appropriate topologies.