On weakly infinite-dimensional subspaces

Volume 140 / 1992

Piet Borst 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.


  • Piet BorstDepartment of Mathematics
    Free University
    De Boelelaan 1081
    1081 HV Amsterdam, The Netherlands

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