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On families of Lindelöf and related subspaces of 2<sup>ω<sub>1</sub></sup>

On families of Lindelöf and related subspaces of 2<sup>ω<sub>1</sub></sup>

We consider the families of all subspaces of size $\omega _1$ of $2^{\omega _1}$ (or of a compact zero-dimensional space $X$ of weight $\omega _1$ in general) which are normal, have the Lindelöf property or are closed under limits of convergent $\omega _1