- 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...
- 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...
- 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...
- p-algebra L, for all x , y ∈ L : {\displaystyle x,y\in L:} The map x ↦ x* is
antitone. In particular, 0* = 1 and 1* = 0. The map x ↦ x** is a closure. x* = x***...
- 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...
-
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...
