Submitted:
02 November 2022
Posted:
03 November 2022
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Abstract
We develop the theory of Heyting small spaces and prove a new version of Esakia duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.
Keywords:
Esakia duality
; small space
; spectral space
; Heyting algebra
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