Extension theory and finite products of copies of

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.