Multimo dal logics of products of topologies

Studia Logica 84 (3) (2006)
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 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.
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Dmitry Sustretov (2009). Hybrid Logics of Separation Axioms. Journal of Logic, Language and Information 18 (4):541-558.

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