Let $X = \prod_{n \in \mathbb{N}} X_n$ be a D326: Cartesian product such that

(i)	$\pi_n$ is a D327: Canonical set projection on $X$ for each $n \in \mathbb{N}$
(ii)	$E \subseteq X$ is a D78: Subset of $X$

Then $\{ x_n \}_{n \in \mathbb{N}} \in E$ if and only if \begin{equation} \forall \, n \in \mathbb{N} : x_n \in \pi_n(E) \end{equation}