 We need first some general preliminaries, and forgetting the intended application(s) for a moment, let us define, given sets S and T, a pair of functions (f, g) to be a Galois connection between S and T when  f: ℘(S) → ℘(T) and g: ℘(T)→ ℘(S), and for all S0, S1 ⊆ S, T0, T1 ⊆ T, we have S0 ⊆ g(f(S0)), T0 ⊆ f(g(T0)), S0 ⊆ S1 ⇒ f(S1) ⊆ f(S0), and T0 ⊆ T1 ⇒ g(T1) ⊆ g(T0). It is well known that the composition of g with f (respectively, f with g) in such a case is a closure operation on S (respectively, on T) in the sense of being a function (we do the S case) C: ℘(S) → ℘(S) satisfying, for all subsets S0, S1, of S: