[[Metric space]]
# Open ball
In any [[metric space]] $(X, d)$, we can define the **open ball** of radius $r$ around a point $a$
$$
\begin{align*}
\mathrm{B}_{r}(a) = \{ x \in X : d(x,a) < r \}
\end{align*}
$$
where $a \in X$, and naturally $r \in \mathbb{R}^+$. #m/def/anal 
The open balls form the [[topological basis]] for a [[Metric topology]].

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#state/tidy | #lang/en | #SemBr