\begin{definition}[Definition:Closed Rectangle]
Let $n \ge 1$ be a natural number.
Let $a_1, \ldots, a_n, b_1, \ldots, b_n$ be real numbers.
The Cartesian product of closed intervals:
:$\ds \prod_{i \mathop = 1}^n \closedint {a_i} {b_i} = \closedint {a_1} {b_1} \times \cdots \times \closedint {a_n} {b_n} \subseteq \R^n$
is called a '''closed rectangle in $\R^n$''' or '''closed $n$-rectangle'''.
\end{definition}