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Subordinations on Bounded Distributive Lattices

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Abstract

In this paper we shall study some classes of bounded distributive lattices endowed with a subordination relation, called subordination lattices. We shall prove that certain algebraic conditions defined in terms of subordinations correspond to first-order conditions on the dual space of a subordination lattice. As a consequence of these correspondences we shall obtain new topological dualities for some known classes of subordination lattices, as for instance the class of proximity lattices studied by M. B. Smyth, or the class of strong proximity lattices studied by A. Jung and P. Sünderhauf. We shall also introduce some new classes of subordination lattices, as the class of compingent lattices and de Vries lattices.

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Acknowledgements

This paper has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 689176, and the support of the grant PIP 11220150100412CO of CONICET (Argentina).

The author is very grateful to the referee for helpful remarks and suggestions.

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  1. Departamento de Matemática and CONICET, Universidad Nacional del Centro, Pinto 399, 7000, Tandil, Argentina

    Sergio A. Celani

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  1. Sergio A. Celani
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Celani, S. Subordinations on Bounded Distributive Lattices. Order 40, 1–27 (2023). https://doi.org/10.1007/s11083-021-09580-5

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