Definition:Bounded Euclidean Space/Unbounded

Definition

Let $A \subseteq \R^n$ be a subset of a Euclidean space under the usual metric.

$A$ is unbounded (in $\R^n$) if and only if $A$ is not bounded (in $\R^n$).

Also see

• Results about unbounded Euclidean spaces can be found here.

Sources

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