Saturated set

In mathematics, in particular in topology, a subset of a topological space (X, τ) is saturated if it is an intersection of open subsets of X. In a T₁ space every set is saturated.

Saturated sets can also be defined in terms of surjections: let p : X → Y be a surjection; a subset C of X is called saturated with respect to p if for every p⁻¹(A) that intersects C, p⁻¹(A) is contained in C. This is equivalent to the statement that p⁻¹p(C)=C.