The closed unit ball of X is compact in the weak topology.

The proportionality constant is the volume of the unit ball.

In this integral, the field γ has been extended so that it is defined on the interior of the unit ball.

Therefore one speaks of "the" unit ball or "the" unit sphere.

Note that for the circumferences of the two-dimensional unit balls we have:

The main problem here is that the unit balls of infinite-dimensional Hilbert spaces are not compact.

In a semi normed vector space the closed unit ball is a barrel.

In other words, is the unit ball in with respect to .

These results then extend to the unit ball deprived of the origin.

Let C denote the complement of the unit ball.