0
0
I was proving the Moore's Plane $(X,\mathscr T)$ is not normal. Using the theorem. Let $C=\{(x,y)\in X:y=0\}$ be a closed and relatively discrete subset of $X$. Let $D=\{(x,y)\in X:x\in \mathbb Q \text{and} y\in \mathbb Q\}$ is a dense subset of $X$. How do I prove that there exists a bijection...
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.
== Definition ==
If
Γ
{\displaystyle \Gamma }
is the (closed) upper half-plane
Γ
=
{
(
x
,
y
)
∈
R
...
