Heyting Locally Small Spaces and Esakia Duality

We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version Esakia duality and system concrete isomorphisms equivalences. In way, we continue building tame topology, realising Grothendieck’s ideas. use up-spectral spaces define standard up-spectralification Kolmogorov space. This research gives more understanding definable over structures with topologies.