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arXiv · 2512.22042

Esakia order-compactifications and locally Esakia spaces

Rodrigo Nicolau Almeida·Guram Bezhanishvili·Nick Bezhanishvili
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Abstract

We introduce Esakia order-compactifications and study how they fit in the general theory of Priestley order-compactifications. We provide an analog of Dwinger's theorem by characterizing Esakia order-compactifications by means of special rings of upsets. These considerations naturally lead to the notion of a locally Esakia space, for which we prove that taking the largest Esakia order-compacification is functorial, thus obtaining an analog of Banaschewski's theorem.

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Rodrigo Nicolau Almeida, Guram Bezhanishvili, Nick Bezhanishvili. 2025-12-26. Esakia order-compactifications and locally Esakia spaces. https://arxiv.org/abs/2512.22042

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