Definition:Product Topology/Factor Space

Definition
Let $\family {\struct {S_i, \tau_i} }_{i \mathop \in I}$ be an indexed family of topological spaces where $I$ is an arbitrary index set.

Let $\struct{S, \tau}$ be the product space of $\family {\struct {S_i, \tau_i} }_{i \mathop \in I}$.

Each of the topological spaces $\struct{S_i, \tau_i}$ are called the factors of $\struct{S, \tau}$, and can be referred to as factor spaces.