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The reflexive closure of a binary relation R on a set X is the minimal reflexive relation R^' on X that contains R. Thus aR^'a for every element a of X and aR^'b for distinct ...

The reflexive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same reflexive closure as R. Thus aR^'b for any elements a and b of X, ...

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...

The transitive reduction of a binary relation R on a set X is the minimum relation R^' on X with the same transitive closure as R. Thus aR^'b for any elements a and b of X, ...

A mathematical relationship transforming a function f(x) to the form f(x+a).

The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

Let X and Y be sets, and let R subset= X×Y be a relation on X×Y. Then R is a concurrent relation if and only if for any finite subset F of X, there exists a single element p ...

Let (a)_i be a sequence of complex numbers and let the lower triangular matrices F=(f)_(nk) and G=(g)_(nk) be defined as f_(nk)=(product_(j=k)^(n-1)(a_j+k))/((n-k)!) and ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If h is one-to-one and is a join-homomorphism, then it is a join-embedding.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. If K=L and h is a join-homomorphism, then we call h a join-endomorphism.