The proof that Moore plane is not normal I have read was using Cantor's nesting theorem. But I heard that it is also possible to use Baire category theorem to prove and I want to know how.
So, as usually, we start with fomulating two sets
$Q = \{(x,0):x\in\mathbb{Q}\}$ and $P = \{(x,0):x\in\mathbb{P}\} $
where $\mathbb{Q}$ is rational number and $\mathbb{P}$ is irrational.
Then how to proceed the next step? Any references would be also appreciated.
Cheers.