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A capital B with a centre and a radius in brackets.
Also known as: Open ball, Ball notation, Metric ball, B of x and r
An open ball is every point within a stated distance of a centre, not including the boundary. It is the basic building block of every metric topology — open sets are unions of these — which is why the notation appears before almost anything else in an analysis course.
Denotes the set of points strictly within a given distance of a given centre in a metric space.
Contexts: Mathematics
Generates the topology of a metric space: the open sets are exactly the unions of open balls.
Contexts: Mathematics
Excludes its boundary; the closed ball, written with a bar or a different letter, includes it.
Contexts: Mathematics
A capital letter B followed by a bracketed pair: a point name and a radius, separated by a comma.