Circular chain

illustration

In mathematics, and especially in function theory , a set of circular disks in the complex plane is called a circular chain if the circular disks are not openly disjoint . They then form a connected component and are an important tool for analytically continuing holomorphic functions that are only defined on the first circular disk . ${\displaystyle (K_{0},\dots ,K_{n})}$ ${\displaystyle K_{0}}$

definition

Let be open circular disks. Their union is a circular chain if one exists for all of them, i.e. the intersection of two consecutive circular disks is not empty . ${\displaystyle K_{0},\ldots ,K_{n}\subset \mathbb {C} }$ ${\displaystyle j<n}$ ${\displaystyle z_{j}\in K_{j}\cap K_{j+1}}$

literature

• Klaus Jänich : Function Theory . 6th edition. Springer , 2004, ISBN 3-540-20392-3 , pp. 46-60 .