Explore: Unit Ball

space; the unit circle is a special case, the unit ⁠ 1 {\displaystyle 1} ⁠-sphere in the plane. An (open) unit ball is the region inside of a unit sphere

a ball (open or closed) always includes p itself, since the definition requires r > 0. A unit ball (open or closed) is a ball of radius 1. A ball in

A ball transfer unit is an omnidirectional load-bearing sphere mounted inside a restraining fixture. They are identical in principle to a computer trackball

R^{n}V_{n},} where V n {\displaystyle V_{n}} is the volume of the unit n-ball, the n-ball of radius 1. The real number V n {\displaystyle V_{n}} can be expressed

the unit ball of X {\displaystyle X} is a proper subset of the unit ball of X ″ . {\displaystyle X''.} The Goldstine theorem states that the unit ball of

)=1\right\}=S^{1}} while the closed unit ball in ( X , d ) {\displaystyle (X,d)} is the union of the open unit ball and the unit sphere centered at this same

the closed unit ball of the dual space of a normed vector space is compact in the weak* topology. A common proof identifies the unit ball with the weak-*

corresponds to a left-handed helicoid. A critical catenoid is a catenoid in the unit ball that meets the boundary sphere orthogonally. Up to rotation about the

the definition of the norm, the unit circle must be convex and centrally symmetric (therefore, for example, the unit ball may be a rectangle but cannot

to be a closed unit ball D n {\displaystyle D^{n}} . For the same reason it holds for every set that is homeomorphic to a closed ball (and therefore also