\begin{definition}[Definition:Open Ball/Real Analysis]
Let $n \ge 1$ be a natural number.
Let $\R^n$ denote a real Euclidean space
Let $\norm \cdot$ denote the Euclidean norm.
Let $a \in \R^n$.
Let $R > 0$ be a strictly positive real number.
The '''open ball of center $a$ and radius $R$''' is the subset:
:$\map B {a, R} = \set {x \in \R^n : \norm {x - a} < R}$
\end{definition}