Once upon a time I asked whether $\omega\_1 \times \beta \mathbb{N}$ is normal. I got the answer no and a fairly convincing proof of this [here](http://at.yorku.ca/cgi-bin/bbqa?forum=ask_a_topologist_2006;task=show_msg;msg=1582.0002)


However I'm currently in a situation where I have three plausible proofs of plausible results at most two of which can be true, and of the three this is the one of which I'm currently the least sure (there are a bunch of details I haven't yet fully checked as I'm in the process of dusting off some of my recently rather unused knowledge about general topology), so was hoping someone could confirm.



Is ω1 × βN normal?
I have reread the proof and it's completely correct. 
The idea is that $\omega\_1 \times \beta\mathbb{N}$ 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. 


