More generally, a point x ∈ X is called a point of discontinuity for the action of G if there is an open subset U ∋ x such that there are only finitely many g ∈ G with g ⋅ U ∩ U ≠ ∅. The domain of discontinuity of the action is the set of all points of discontinuity. Equivalently it is the largest G -stable open subset Ω ⊂ X such that the action of G on Ω is wandering. In a dynamical context this is also called a wandering set.