Complex sentence: Note that here, a box is a generalized rectangle on a multidimensional space, formally defined as a cartesian product of linear intervals, which eventually build up the same box we have been talking about.
Split into simpler sentences: Note that here, a box is something like a generalized rectangle on a multidimensional space. You can even formally define it as a cartesian product of linear intervals, which eventually build up the same box we have been talking about.