Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

Streszczenie

We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and $dim Y = ω_0$ and $dim X = ω_0 + 1$. Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.