Definition:Cartesian Product/Uncountable

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

Let $\left\langle{\left({S_\alpha}\right)}\right \rangle_{\alpha \mathop \in I}$ be a family of sets indexed by $I$.

The cartesian product of $\left \langle {S_\alpha} \right \rangle$ is denoted:


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