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.
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.