\begin{definition}[Definition:Final Topology]
Let $X$ be a set.
Let $I$ be an indexing set.
Let $\family {\struct{Y_i, \tau_i}}_{i \mathop \in I}$ be an $I$-indexed family of topological spaces.
Let $\family {f_i: Y_i \to X}_{i \mathop \in I}$ be an $I$-indexed family of mappings.
\end{definition}