sphere (metric space)
The set is called the sphere of radius with centre . This generalizes the notion of spheres to metric spaces.
Note that the sphere in a metric space need not look like a sphere in Euclidean space. For instance, if we impose the metric on instead of the Euclidean metric, spheres according to this metric are actually cubes! Even more bizarre situations can occur in general — a sphere might be disconnected, or it may be discrete, or it may even be an empty set.
|Title||sphere (metric space)|
|Date of creation||2013-03-22 14:47:38|
|Last modified on||2013-03-22 14:47:38|
|Last modified by||rspuzio (6075)|