\begin{definition}[Definition:Product Topology/Factor Space]
Let $\family {\struct {X_i, \tau_i} }_{i \mathop \in I}$ be an indexed family of topological spaces where $I$ is an arbitrary index set.
Let $\struct {\XX, \tau}$ be the product space of $\family {\struct {x_i, \tau_i} }_{i \mathop \in I}$.
Each of the topological spaces $\struct {X_i, \tau_i}$ are called the '''factors''' of $\struct {\XX, \tau}$, and can be referred to as '''factor spaces'''.
\end{definition}