Orbit space

Given a group $𝐺$ acting on a space $𝑋$ , the orbit space¹ or quotient $𝑋 / 𝐺$ is the set of orbits partitioning $𝑋$ . #m/def/group If $𝑋$ is a topological space, $𝑋 / 𝐺$ is typically endowed with the quotient topology induced by the projection $𝑝 : 𝑥 \mapsto 𝐺 𝑥$ .