Abstract
For each ordinal $1 \leq \alpha < \omega_1$ we present separable metrizable spaces $X_\alpha, Y_\alpha$ and $Z_\alpha$ such that (i) ${\rm f}\,X_\alpha$, f $Y_\alpha$, f $Z_\alpha = \omega_0$, where $\rm f$ is either $\rm trdef$ or ${\cal K}_0\mbo
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