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Heyting Locally Small Spaces and Esakia Duality
Version 1
: Received: 1 June 2023 / Approved: 2 June 2023 / Online: 2 June 2023 (09:40:30 CEST)
A peer-reviewed article of this Preprint also exists.
Piękosz, A. Heyting Locally Small Spaces and Esakia Duality. Symmetry 2023, 15, 1342. Piękosz, A. Heyting Locally Small Spaces and Esakia Duality. Symmetry 2023, 15, 1342.
Abstract
We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version of Esakia duality and a system of concrete isomorphisms and equivalences. In such a way, we continue building tame topology, realising Grothendieck's ideas. We use up-spectral spaces and define the standard up-spectralification of a Kolmogorov locally small space. This research gives more understanding of locally definable spaces over structures with topologies.
Keywords
tame topology; Esakia duality; locally small space; up-spectral space
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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