Definition:Compact Space/Metric Space/Complex
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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
- 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: $4.$