Definition:Totally Bounded Metric Space/Definition 2
Jump to navigation
Jump to search
Definition
A metric space $M = \struct {A, d}$ is totally bounded if and only if:
- for every $\epsilon \in \R_{>0}$ there exist finitely many points $x_0, \dots, x_n \in A$ such that:
- $\ds \inf_{0 \mathop \le i \mathop \le n} \map d {x_i, x} \le \epsilon$
- for all $x \in A$.
Also known as
A totally bounded metric space is also referred to as a precompact space.
Also see
- Results about totally bounded metric spaces can be found here.