Definition:Open Ball/Real Analysis

Definition
Let $n\geq1$ be a natural number.

Let $\R^n$ denote real Euclidean space

Let $\|\cdot\|$ 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:
 * $B(a, R) = \{x \in \R^n : \Vert x-a \Vert < R\}$

Also see

 * Definition:Closed Ball (Real Analysis)
 * Definition:Open Set (Real Analysis)