--- tags: definition Created: 2023-09-01 Modified: 2023-09-01 mathLink: auto #definition #geometry-topology/point-set-topology --- > [!definition] > Suppose $(X, d)$ is a [[metric space]]. A subset $A \subset X$ is said to be **bounded** if there exists $M \in \mathbb{R}$ such that $d(a_{1},a_{2}) \leq M$ for all pairs $(a_{1},a_{2})$ of points in $A$. >