# Ball (mathematics)

In a metric topology, a ball of radius r centered at a point p is the set of all points at distance at most r from p. In symbolic notation:

$Ball(p,r)=\{x| d(x,p)\le r\}$

where d is the distance function (i.e. metric). Balls are the basic open sets of a metric topology.

If the topology is the Euclidean space, then the boundary (surface) of a ball is a sphere.