Any finitely connected bounded region in the plane is conformally equivalent to the open unit disk with finitely many smaller disjoint closed disks removed; this result is known as Koebe's "Kreisnormierungs" theorem.
Any finitely connected bounded region in the plane is conformally equivalent to the open unit disk with finitely many smaller disjoint. Closed disks removed finitely many smaller disjoint. This result is known as Koebe's "Kreisnormierungs" theorem. Koebe's theorem also implies this.