# Open Balls

##### Updated: October 21, 2020

Let \((X, d)\) be a metric space. Let \(a \in X\) and \(\delta > 0\). The subset of \(X\) consisting of those points \(x \in X\) such that \(d(a, x) < \delta\) is the called the *open ball* of radius \(\delta\) and denoted:

\begin{equation} B(a;\delta) \end{equation}