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monotone. The dual notion is often called antitone, anti-monotone, or order-reversing. Hence, an antitone function f satisfies the property x ≤ y ⟹ f...

this article, we will refer to them as (monotone) Galois connections and antitone Galois connections. A Galois connection is rather weak compared to an order...

implies a ≤ b. On the other hand, a function may also be order-reversing or antitone, if a ≤ b implies f(a) ≥ f(b). An order-embedding is a function f between...

having all operations in O as a polymorphism. Pol and Inv together form an antitone Galois connection. For any finite set Γ of relations over a finite domain...

the intersection of the kernels of the χ with χ(P) = 1. This gives an (antitone) Galois connection between monogenic closed subgroups of T (those with...

f : A → B° and f *: B° → A form a Galois connection under the original antitone definition of this notion. If f : A → B and g : B → C are residuated mappings...

\operatorname {V} (S)\iff S\subset \operatorname {I} (X),} and so V and I form an antitone Galois connection between subsets of polynomials in k [ x 1 , … , x n ]...

if x R y and y R x implies x = y, for all elements x, y in X. Antitone. An antitone function f between posets P and Q is a function for which, for all...

ordered sets is called a Galois connection (or, if it is contravariant, an antitone Galois connection). See that article for a number of examples: the case...

{\displaystyle x,y\in L:} The map x ↦ x ∗ {\displaystyle x\mapsto x^{*}} is antitone. In particular, 0 ∗ = 1 {\displaystyle 0^{*}=1} and 1 ∗ = 0 {\displaystyle...

sublattice; (b) the cost function of each player is submodular and has antitone differences. Topkis proves, using fixed-point arguments, that some submodular...