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Keywords:
forcing; topology; products; Lindelöf
forcing; topology; products; Lindelöf
Summary:
We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space $X$ whose square $X^2$ is again Lindelöf but its cube $X^3$ has a closed discrete subspace of size ${\frak c}^+$, hence the Lindelöf degree $L(X^3) = {\frak c}^+ $. In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space $X$ such that $L(X^n) = \aleph_0$ for all positive integers $n$, but $L(X^{\aleph_0}) = {\frak c}^+ = \aleph_2$.
References:
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