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arXiv · 2604.20603

Topological Dualities for Modal Algebras

Matthew Collinson
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Abstract

We display a family of Stone-type dualities linking categories of frames carrying pairs of modal operators to categories of spaces carrying a binary relation. Different notions of morphism used on the relational side lead to significant variations in the point construction. We show how the situation simplifies in the case of semicontinuous relations, allowing for straightforward correspondences between modal axioms and relational properties.

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Matthew Collinson. 2026-04-22. Topological Dualities for Modal Algebras. https://arxiv.org/abs/2604.20603

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