Definition:Product Topology/Factor Space

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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.