Category:Definitions/Bounded Euclidean Spaces

This category contains definitions related to Bounded Euclidean Spaces.
Related results can be found in Category:Bounded Euclidean Spaces.

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

$A$ is bounded (in $\R^n$) if and only if :

$\exists N \in \R: \forall x \in A: \size x \le N$

That is, every element of $A$ is within a finite distance of any point we may choose for the origin.