Definition:Agreement of Relations

Definition

Let:

• $\mathcal R_1 \subseteq S_1 \times T_1$ be a relation on $S_1 \times T_1$
• $\mathcal R_2 \subseteq S_2 \times T_2$ be a relation on $S_2 \times T_2$
• $X \subseteq S_1 \cap S_2$

If:

$\forall s \in X: \mathcal R_1 \left ({s}\right) = \mathcal R_2 \left ({s}\right)$

then the relations $\mathcal R_1$ and $\mathcal R_2$ are said to agree on or be in agreement on $X$.

Note

The concept is usually seen in the context of mappings.

Sources

• George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$