Definition:Bounded Metric Space/Complex
< Definition:Bounded Metric Space(Redirected from Definition:Bounded Subset of Complex Plane)
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Definition
Let $D$ be a subset of the complex plane $\C$.
Then $D$ is bounded (in $\C$) if and only if there exists $M \in \R$ such that:
- $\forall z \in D: \cmod z \le M$
Unbounded
Let $D$ be a subset of the complex plane $\C$.
Then $D$ is unbounded (in $\C$) if and only if:
- $\nexists M \in \R: \forall z \in D: \cmod z \le M$
That is, if $D$ is not bounded in $\C$.
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Point Sets: $4.$