Homogeneous relation

In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian...

A binary relation is called a homogeneous relation when X = Y {\displaystyle X=Y} . A binary relation is also called a heterogeneous relation when it is...

a < c; and if x = y and y = z then x = z. A homogeneous relation R on the set X is a transitive relation if, for all a, b, c ∈ X, if a R b and b R c,...

algebra, homogeneous polynomials have the same number of factors of a given kind. In the study of binary relations, a homogeneous relation R is on a...

which every pair is comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially...

relation concept described above is obtained; it is often called homogeneous relation (or endorelation) to distinguish it from its generalization. The...

strongly connected as defined above. Let R {\displaystyle R} be a homogeneous relation. The following are equivalent: R {\displaystyle R} is strongly connected;...

reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to...

Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...

mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in...