Definition:Union Mapping/Finite Set

Definition

Let $S = \set {f_1, f_2, \ldots, f_n}$ denote a finite set of mappings.

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

$\forall i, j \in \set {1, 2, \ldots, n}: f_i$ and $f_j$ are combinable

and is defined as:

$\forall x \in \ds \bigcup \set {\Dom {f_i}: i \in \set {1, 2, \ldots, n} } x \in \Dom {f_i} \implies f = \map {f_i} x$

Sources

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