Let G be a group and S be a topological G-set. Then a closed subset F of S is called a fundamental domain of G in S if S is the union of conjugates of F, i.e., S = union _(g element G) g F, and the intersection of any two conjugates has no interior. For example, a fundamental domain of the group of rotations by multiples of 180° in R^2 is the upper half-plane {(x, y)|y>=0} and a fundamental domain of rotations by multiples of 90° is the first quadrant {(x, y)|x, y>=0}. The concept of a fundamental domain is a generalization of a minimal group block, since while the intersection of fundamental domains has empty interior, the intersection of minimal blocks is the empty set.

group block | G-set