Open Ball

An -dimensional open ball of radius  is the collection of points of distance less than  from a fixed point in Euclidean -space. Explicitly, the open ball with center  and radius  is defined by

The open ball for  is called an open interval, and the term open disk is sometimes used for  and sometimes as a synonym for open ball.

REFERENCES:

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 1, 1991.