Definition:Union Mapping

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 $T_2$

Let $f_1$ and $f_2$ be combinable, that is, that they agree on $S_1 \cap S_2$.

Then the union mapping $f = f_1 \cup f_2$ of $f_1$ and $f_2$ is:


 * $f: S_1 \cup S_2 \to T_1 \cup T_2: \map f s = \begin{cases}

\map {f_1} s : & s \in S_1 \\ \map {f_2} s : & s \in S_2 \end{cases}$

Also known as
The union mapping (of $f_1$ and $f_2$) can also be seen referred to as the combined mapping (of $f_1$ and $f_2$).

Also see

 * Definition:Union of Mappings
 * Definition:Union Relation