## Coursera Complex Analysis 1.5 Terminology

### Jul 4, 2016

$B_r(z_0)$ disk radius r, centre $z_0$, excluding boundary. $|z - z_0| < r$

$K_r(z_0)$ circle radius r, centre $z_0$, . $|z - z_0| = r$

Interior point. E is some subset of the complex plane. $z_0$ is an interior point of E if there is some r > 0 such that the disc around $z_0$ is in E, i.e. $B_r(z_0) \subset E$ .

Boundary point. E is some subset of the complex plane. b is a boundary point of E if every disc around b contains a point in E and a point not in E.

The set of all boundary points is $\partial E$.

A set is open if every one of its points are interior.

A set is closed if it contains all its boundary points.

Closure

Interior