In closure spaces (thus, also in topological spaces), one may define the boundary of a set A as the closure of A minus the interior of A. This set is partitioned into "the closure of A minus A" and "A minus the interior of A", that are equal, respectively, to "the boundary of A intersected with the complement of A" and "the boundary of A intersected with A".

Do these two sets partitioning a boundary have a common name? Who studied them?