# Definition:Product Space (Topology)/Factor Space

(Redirected from Definition:Factor Space)
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.