Definition:Agreement/Mappings

Definition

Let:

$(1): \quad f_1: S_1 \to T_1$ be a mapping from $S_1$ to $T_1$

$(2): \quad f_2: S_2 \to T_2$ be a mapping from $S_2$ to $T_2$

$(3): \quad X \subseteq S_1 \cap S_2$

Let:

$\forall s \in X: \map {f_1} s = \map {f_2} s$

Then the mappings $f_1$ and $f_2$ are said to agree on or be in agreement on $X$.

Sources

• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Restrictions and Extensions
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): agree
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): agree
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): agree