Intrinsic boundary of a simply connected domain ($\delta D=\hat{D}\setminus D$)

Choose a conformal map from a proper simply connected domain to the unit disc and pull back the topology of the closed disc. The resulting compactification is independent of the chosen map, since disc automorphisms extend to its boundary. Its intrinsic boundary distinguishes different approaches to a slit. Every conformal map between such domains extends to their intrinsic compactifications. This boundary agrees with the prime-end description in the simply connected setting.