Doubly connected domain ($|{\pi }_0(\hat{\mathbb{C}}\setminus \Omega )|=2$)

A planar domain whose complement in the Riemann sphere has exactly two connected components. An annulus is the standard example. If neither complementary component is a single point, the domain is conformally equivalent to a circular annulus with finite positive conformal modulus of an annulus; punctured-disc and punctured-plane cases account for degenerate complementary components.