Ball (mathematics)
 

A ball is the volume space bounded by a sphere;
it is also called a solid sphere.[1]
It may be a closed ball (including the boundary points that constitute the sphere)
or an open ball (excluding them).

These concepts are defined not only in three-dimensional Euclidean space
but also for lower and higher dimensions, and for metric spaces in general.

A ball or hyperball in n dimensions is called an n-ball
and is bounded by an (n − 1)-sphere.
Thus, for example, a ball in the Euclidean plane is the same thing as a disk,
the area bounded by a circle.

In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere.
In a one-dimensional space, a ball is a line segment.

Closed ball

In a metric space, a closed set about a point x which consists of all points
that are equal to or less than a fixed distance from x.

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