sphere (metric space)

The set {xd(x,c)=r} is called the sphere of radius r with centre c. 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 d(x,y)=max{|x1-y1|,|x2-y2|,|x3-y3|} on 3 instead of the Euclidean metricMathworldPlanetmath, 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 setMathworldPlanetmath.

Title sphere (metric space)
Canonical name SpheremetricSpace
Date of creation 2013-03-22 14:47:38
Last modified on 2013-03-22 14:47:38
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Definition
Classification msc 54E35
Synonym sphere