Definition:Metrizable Tangent Disc Topology
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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
- Results about the metrizable tangent disc topology can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {II}$: Counterexamples: $83$. Metrizable Tangent Disc Topology