Definition:Bounded Metric Space

Definition
Let $M = \left({X, d}\right)$ be a metric space.

Let $M' = \left({Y, d_Y}\right)$ be a subspace of $M$.

Complex Plane
From Complex Plane is Metric Space, this concept can be applied directly to the complex plane:

Also known as
If the context is clear, it is acceptable to use the term bounded space for bounded metric space.

Also see

 * Equivalence of Definitions of Bounded Metric Space


 * Element in Bounded Metric Space has Bound


 * Definition:Totally Bounded
 * Definition:Uniformly Bounded


 * Boundedness of Metric Space by Open Ball


 * Definition:Diameter of Bounded Metric Subspace


 * Definition:Bounded Mapping to Metric Space