Nemytskii 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 a completely regular Hausdorff space (also called Tychonoff space) that is not normal. It is named after Robert Lee Moore and Viktor Vladimirovich Nemytskii.

If ${\displaystyle \Gamma }$ is the (closed) upper half-plane ${\displaystyle \Gamma =\{(x,y)\in \mathbb {R} ^{2}|y\geq 0\}}$, then a topology may be defined on ${\displaystyle \Gamma }$ by taking a local basis ${\displaystyle {\mathcal {B}}(p,q)}$ as follows:

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