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arXiv · 2607.10323

A bitopological duality for some subordination Boolean algebras

Sergio A. Celani
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Abstract

S4-subordination algebras are a generalization of the closure algebras. In this paper, we give a topological representation for S4-subordination algebras by means of bitopological spaces $\left $, where $\left $ is a Stone space and $\tau_{S}$ is a topology that enables the characterization of the subordination relation. We apply this bitopological representation to give a characterization of S5-subordination algebras and lattice subordinations. We also show that there exists a bijective correspondence between congruence compatible with the subordination and certain closed subsets of the Stone space $\left $ that are also saturated sets of the space $\left $. Additionally, we explore two types of morphisms between S4-subordination algebras: one based on Boolean homomorphisms and another based on meet-homomorphisms. Finally, we provide a topological representation for each type of morphism.

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Sergio A. Celani. 2026-07-11. A bitopological duality for some subordination Boolean algebras. https://arxiv.org/abs/2607.10323

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