Unit ball

In mathematics, the open unit ball in a normed vector space for a given norm is

The closed unit ball on under is

The 'shape' of the unit ball is entirely dependent on the chosen norm; it may well have 'corners', and for example may look like [−1,1]ⁿ, in the case of the norm l_∞ in Rⁿ. The round ball is understood as the usual Hilbert space norm, based in the finite dimensional case on the Euclidean distance; its boundary is what is usually meant by the unit sphere.

See also:

unit circle
unit square
unit disk
sphere
ball (mathematics)
Table of mathematical symbols

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