Sober space
TOPOLOGICAL SPACE WHOSE TOPOLOGY IS FULLY CAPTURED BY ITS LATTICE OF OPEN SETS
Irreducible subset; Irreducible (topology); Sober topological space
In mathematics, a sober space is a topological space X such that every (nonempty) irreducible closed subset of X is the closure of exactly one point of X: that is, every irreducible closed subset has a unique generic point.