In
mathematics, a
unit sphere is the set of points of
distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed
unit ball is the set of points of
distance less than or equal to 1 from a fixed central point. Usually a specific point has been distinguished as the
origin of the space under study and it is understood that a unit sphere or unit ball is centered at that point. Therefore one speaks of "the" unit ball or "the" unit sphere.