Definition:Coreflexive Relation

Definition

Let $\RR \subseteq S \times S$ be a relation in $S$.

Definition 1

$\RR$ is coreflexive if and only if:

$\forall x, y \in S: \tuple {x, y} \in \RR \implies x = y$

Definition 2

$\RR$ is coreflexive if and only if:

$\RR \subseteq \Delta_S$

where $\Delta_S$ is the diagonal relation.

Also see

• Equivalence of Definitions of Coreflexive Relation

• Definition:Reflexivity

• Definition:Reflexive Relation
• Definition:Antireflexive Relation
• Definition:Non-Reflexive Relation

• Results about coreflexive relations can be found here.

Linguistic Note

Coreflexive is pronounced co-reflexive, not core-flexive.