# Definition:Closed Set/Complex Analysis

This page is about Closed Set in the context of Complex Analysis. For other uses, see Closed.

## Definition

Let $S \subseteq \C$ be a subset of the complex plane.

$S$ is closed (in $\C$) if and only if every limit point of $S$ is also a point of $S$.

That is: if and only if $S$ contains all its limit points.

## Examples

### Closed Unit Circle

Let $S$ be the subset of the complex plane defined as:

$\cmod z \le 1$

where $\cmod z$ denotes the complex modulus of $z$.

Then $S$ is closed.