Extension theory and finite products of copies of [0,Ω)

We study products of the first uncountable ordinal space [0,Ω) with itself. We show that any product of copies of [0,Ω) is pseudo-compact and note the classical result that any countable product of copies of [0,Ω) is normal. Our Main Result yields that if X is a finite product of copies of [0,Ω), Z is a compact metrizable space, and K is a CW-complex with K an absolute extensor for Z, then K is an absolute extensor for Y=Z×X. It will also show that K is an absolute extensor for the Stone–Čech compactification, β(Y), of Y.