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:

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

Sources

• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Restrictions and Extensions