\begin{definition}[Definition:Metrizable Tangent Disc Topology]
Let $A$ be a countable subset of the $x$-axis in the Cartesian plane $\R^2$.
Let $P$ denote the open upper half-plane in $\R^2$.
Let $S := A \cup P$.
Let $\struct {S, \tau}$ be the topological subspace of the Niemytzki plane.
$\struct {S, \tau}$ is referred to as the '''metrizable tangent disc topology'''.
\end{definition}