Arrangement (space partition)

In discrete geometry, an arrangement is the decomposition of the d-dimensional linear, affine, or projective space into connected cells of different dimensions, induced by a finite collection of geometric objects, which are usually of dimension one less than the dimension of the space, and often of the same type as each other, such as hyperplanes or spheres. == Definition == For a set A {\displaystyle A} of objects in R d {\displaystyle \mathbb {R} ^{d}} , the cells in the arrangement are the connected components of sets of the form ( ∩ X ) ∖ ∪ ( A ∖ X ) {\displaystyle (\cap X)\setminus \cup (A\setminus X)} for subsets X {\displaystyle X} of A {\displaystyle A} .

Source: Wikipedia — Arrangement (space partition) (CC BY-SA 4.0)