Definition:Reflexive Relation/Definition 2

Definition

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

$\RR$ is reflexive if and only if it is a superset of the diagonal relation:

$\Delta_S \subseteq \RR$

Also see

• Equivalence of Definitions of Reflexive Relation

• Results about reflexive relations can be found here.

Sources

• 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Relations
• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 10$: Inverses and Composites
• 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Relations