Glossary of Order Theory - G

  • Galois connection. Given two posets P and Q, a pair of monotone functions F:PQ and G:QP is called a Galois connection, if F(x) ≤ y is equivalent to xG(y), for all x in P and y in Q. F is called the lower adjoint of G and G is called the upper adjoint of F.
  • Greatest element. For a subset X of a poset P, an element a of X is called the greatest element of X, if xa for every element x in X. The dual notion is called least element.
  • Ground set. The ground set of a poset (X, ≤) is the set X on which the partial order ≤ is defined.

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