Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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