Definition:Cartesian Product/Uncountable

Definition
Let $I$ be an indexing set with uncountable cardinality.

Let $\family {S_\alpha}_{\alpha \mathop \in I}$ be a family of sets indexed by $I$.

The cartesian product of $\family {S_\alpha}$ is denoted:


 * $\displaystyle \prod_{\alpha \mathop \in I} S_\alpha$