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}