Alexandrov topology:
Open sets = upper sets (upsets)
U open ⟺ x∈U, x≤y ⟹ y∈U

Principal upset ↑x:
↑x = {y : x ≤ y}

Specialization order:
x ⤳ y ⟺ y ∈ cl({x})
⟺ x ≤ y in poset

Finite T₀-space ↔ poset
(Alexandrov 1937)

Opens = arbitrary unions
of principal upsets ↑x