Definition:Bounded Metric Space/Definition 2

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Definition

Let $M = \struct {A, d}$ be a metric space.

Let $M' = \struct {B, d_B}$ be a subspace of $M$.


$M'$ is bounded if and only if:

$\exists K \in \R: \forall x, y \in M': \map {d_B} {x, y} \le K$

That is, there exists a finite distance such that all pairs of elements of $B$ are within that distance.


Also see


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