gn.general topology - Is ω1 × βN normal?

I have reread the proof and it's completely correct.
The idea is that $omega_1 times betamathbb{N}$ maps perfectly onto
a non-normal space, and normality is preserved under perfect maps.
Tamano's theorem says that $X$ is paracompact Hausdorff iff $X times beta X$ is normal,
and we use that $omega_1$ is not paracompact and $beta omega_1 = omega_1 + 1$. But the direct proof as sketched is also correct (we can use the pushdown lemma to prove it).

All building blocks can be found in Engelking, e.g.