# 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