90 名前：m binary relations Suppose X and Y are arbitrary sets and a binary relation R over X and Y is given. For any subset M of X, we define F(M) = {y ∈ Y | mRy ∀m ∈ M}. Similarly, for any subset N of Y, define G(N) = {x ∈ X | xRn ∀n ∈ N}. Then F and G yield an antitone Galois connection between the power sets of X and Y, both ordered by inclusion ⊆.
Up to isomorphism all antitone Galois connections between power sets arise in this way. This follows from the "Basic Theorem on Concept Lattices". Theory and applications of Galois connections arising from binary relations are studied in formal concept analysis. That field uses Galois connections for mathematical data analysis.
