open ball
The open ball \(B\), is defined as
\begin{equation}
B(\hat{x}, \delta) = \{x | d(x, \hat{x}) < \delta \}
\end{equation}
Where \(d\) is the (maybe euclidean) distance norm.
In other words, it represents a sphere of values with center \(\hat{x}\) and radius \(\delta\) not including the actual boundary of the ball.
It is an open set, due to the definition of the open set.