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In mathematics, the open unit ball in a normed vector space V for a given
norm
is
- .
The closed unit ball on V 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.
See also:
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