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( Ball (mathematics))
In mathematics, a ball is the inside of a sphere; both concepts apply not only in the three-dimensional space but also for lower and higher dimensions, and for metric spaces in general. Let (M,d) be a metric space, namely a set M with a metric (distance function) d. The open (metric) ball of radius r > 0 centered at a point p in M, usually denoted by Br(p) or B(p;r), is defined by The closed (metric) ball, which may be denoted by Br[p] or B[p;r], is defined by Note in particular that a ball (open or closed) always includes p itself, since the definition requires r > 0.
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Ball (mathematics) Articles
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