On weakly infinite-dimensional subspaces
Volume 140 / 1992
Fundamenta Mathematicae 140 (1992), 225-235 DOI: 10.4064/fm-140-3-225-235
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.