# Definition(s)
> [!NOTE] Definition 1 (Open Euclidean Ball)
> The open ball of radius $r>0$ *centered* at $a\in \mathbb{R}^n$ is given by $\mathbb{B}_{r}(a):=\{ x\in \mathbb{R}^n : \Vert x-a \Vert <r \}.$
**Notation**: We may write $\mathbb{B}(a,r)$ instead of $\mathbb{B}_{r}(a).$
> [!Example] Example
> Contents
# Properties(s)
# Application(s)
**More examples**:
# Bibliography