Let $\mathcal{S}$ be the set of all "closed intervals" in $\mathbb{R}^n$ of the form $[a,b]$, where $a, b \in \mathbb{R}^n$. Let $\mathcal{D}$ be the set whose elements are the following:
A.) All elements of $\mathcal{S}$
B.) $\lim_i A_i$, where $A_i \in \mathcal{S}$ and $\{A_i\}$ is either increasing or decreasing.
Then what are all the elements of $\mathcal{D}$ of type B? In $\mathbb{R}$, this is easy. All limits of increasing and decreasing closed intervals is either any interval, singleton, empty set, infinite intervals (such as $(1, \infty)$), or $\mathbb{R}$. In $\mathbb{R}^2$, these may be any rectangle, point, empty set, the whole $\mathbb{R}^2$, or a 'rectangle' with at least one side (but not all sides) extending to infinity. How to generalize this in $\mathbb{R}^n$? Is it possible to obtain all borel sets in this way?