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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

▾ Set distance

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Basic binary operation

▾ Unsigned basic binary operation

▾ Semimetric

▾ Metric

▾ Metric space

▾ Set distance

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}

The

Child definitions