\begin{definition}[Definition:Deleted Radius Topology]
Let $\struct {\R^2, \tau_d}$ be the real number plane with the usual (Euclidean) topology induced by the Euclidean metric $d$.
Let $\BB$ be the sub-basis of $\tau_d$ defined as the set of all open balls of $\struct {\R^2, d}$ with the horizontal radii to the right of the centers excluded.
Let $\tau$ be the topology generated from $\BB$.
$\tau$ is referred to as the '''deleted radius topology'''.
\end{definition}