Closed Box in $\mathbb{R}^n$

Let $n\in\mathbb{N}$. For each index $i\in\{1,\dots,n\}$, let $a_i,b_i\in\mathbb{R}$ satisfy $a_i\le b_i$. The subset

$$B=\{x=(x_1,\dots,x_n)\in\mathbb{R}^n : a_i\le x_i\le b_i \text{ for every } i\in\{1,\dots,n\}\}$$

is called the closed box in $\mathbb{R}^n$ determined by the endpoints $a_1,b_1,\dots,a_n,b_n$.