In mathematics, Esakia spaces are special ordered topological spaces introduced and studied by Leo Esakia in 1974.
[1] Esakia spaces play a fundamental role in the study of Heyting algebras, primarily by virtue of the Esakia duality—the dual equivalence between the category of Heyting algebras and the category of Esakia spaces.
There are several equivalent ways to define Esakia spaces.
[3] Let (X,≤) and (Y,≤) be partially ordered sets and let f : X → Y be an order-preserving map.
The map f is a bounded morphism (also known as p-morphism) if for each x∈ X and y∈ Y, if f(x)≤ y, then there exists z∈ X such that x≤ z and f(z) = y. Theorem:[4] The following conditions are equivalent: Let (X, τ, ≤) and (Y, τ′, ≤) be Esakia spaces and let f : X → Y be a map.