▾ Set of symbols
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▾ Zermelo-Fraenkel set theory
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▾ Semimetric
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▾ Metric space
▾ Set distance
Closed ball
Formulation 0
Let $M = (X, d)$ be a D1107: Metric space.
The closed ball in $M$ with centre $E \subseteq X$ and radius $r \in (0, \infty)$ is the D11: Set \begin{equation} B_d[E, r] : = \{ x \in X : d(E, x) \leq r \} \end{equation}
Child definitions
» D127: Open ball
» D1401: Sphere