Moore plane

In mathematics, the Moore plane, also sometimes called Niemytzki plane (or Nemytskii plane, Nemytskii's tangent disk topology), is a topological space.

It is an example of a Moore space that is not metrizable.

It is named after Robert Lee Moore and Viktor Vladimirovich Nemytskii.

as follows: That is, the local basis is given by Thus the subspace topology inherited by

is not normal can be established by the following counting argument (which is very similar to the argument that the Sorgenfrey plane is not normal): In fact, if X is a separable topological space having an uncountable closed discrete subspace, X cannot be normal.