\begin{definition}[Definition:Complex Disk/Open]
Let $a \in \C$ be a complex number.
Let $R > 0$ be a real number.
The '''open (complex) disk of center $a$ and radius $R$''' is the set:
:$\map B {a, R} = \set {z \in \C: \cmod {z - a} < R}$
where $\cmod {\, \cdot \,}$ denotes complex modulus.
\end{definition}