Definition:Closed Rectangle

Definition
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.

Also known as
A convenient abbreviation is $\sqbrk {\closedint {\mathbf a} {\mathbf b} }$ for $\ds \prod_{i \mathop = 1}^n \closedint {a_i} {b_i}$.

Also see

 * Definition:Open Rectangle
 * Definition:Half-Open Rectangle