1 Answers
In mathematics, particularly in the subfields of set theory and topology, a set C {\displaystyle C} is said to be saturated with respect to a function f : X → Y {\displaystyle f:X\to Y} if C {\displaystyle C} is a subset of f {\displaystyle f} 's domain X {\displaystyle X} and if whenever f {\displaystyle f} sends two points c ∈ C {\displaystyle c\in C} and x ∈ X {\displaystyle x\in X} to the same value then x {\displaystyle x} belongs to C {\displaystyle C} = f {\displaystyle f=f} then x ∈ C {\displaystyle x\in C} ]. Said more succinctly, the set C {\displaystyle C} is called saturated if C = f − 1 ] . {\displaystyle C=f^{-1}].}
In topology, a subset of a topological space {\displaystyle } is saturated if it is equal to an intersection of open subsets of X . {\displaystyle X.} In a T1 space every set is saturated.