Definition:Union Mapping/Family

Definition
Let $I$ be an indexing set.

Let $F = \family {f_i}_{i \mathop \in I}$ be a family of mappings indexed by $I$

The union mapping $f$ of $F$ is defined when:


 * $\forall i, j \in I: f_i$ and $f_j$ are combinable

and is defined as:


 * $\forall x \in \ds \bigcup \set {\Dom {f_i}: i \in I} x \in \Dom {f_i} \implies f = \map {f_i} x$