Half-open subsets of ℝⁿ

Set

 context $p\in \mathbb N$
 definiendum $\mathfrak J^p\equiv\{\ ]a,b]\ |\ a,b\in\mathbb R^p\ \land\ a\le b\}$

Discussion

This set is one which generates the $\sigma$-Algebra $\mathcal B^p$ of Borel subset of $\mathbb R^p$.

We also write

 definiendum $\mathfrak J\equiv \mathfrak J^1$