Definition:Bounded Metric Space/Definition 1
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Definition
Let $M = \left({A, d}\right)$ be a metric space.
Let $M' = \left({B, d_B}\right)$ be a subspace of $M$.
$M'$ is bounded (in $M$) if and only if:
- $\exists a \in A, K \in \R: \forall x \in B: d \left({x, a}\right) \le K$
That is, there exists an element of $A$ within a finite distance of all elements of $B$.
Also see
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2.2$: Examples: Definitions $2.2.12$