Definition:Compact Space/Metric Space/Complex

Definition

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

Then $D$ is compact (in $\C$) if and only if:

$D$ is closed in $\C$

and

$D$ is bounded in $\C$.

Also see

• Complex Plane is Metric Space

• Results about compact spaces can be found here.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Point Sets: $4.$