Definition:Metrizable Tangent Disc Topology

Definition
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.

Also see

 * Metrizable Tangent Disc Topology is Topology