The

**open 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) < r \} \end{equation}

Definition D127

Open ball

Formulation 0

Let $M = (X, d)$ be a D1107: Metric space.

The**open 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) < r \}
\end{equation}

The