Definition:Bounded Metric Space/Unbounded

Definition

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

Let $M' = \struct {Y, d_Y}$ be a subspace of $M$.

Then $M'$ is unbounded (in $M$) if and only if $M'$ is not bounded in $M$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bounded set
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bounded set