Definition:Totally Bounded Metric Space

Also known as
A totally bounded metric space is also referred to as a precompact space.

Also see

 * Equivalence of Definitions of Totally Bounded Metric Space


 * Totally Bounded Metric Space is Bounded, but the converse is not true. (The simplest example is a countable set with the standard discrete metric.)


 * Metric Space Compact iff Complete and Totally Bounded.