Geodesic
On powers of Lindelöf spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 383-401.

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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 $L(X^{\aleph_0}) = {\frak c}^+ = \aleph_2$.
Classification : 03E35, 54A35, 54B10, 54D20
Keywords: forcing; topology; products; Lindelöf 
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     author = {Gorelic, Isaac},
     title = {On powers of {Lindel\"of} spaces},
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Gorelic, Isaac. On powers of Lindelöf spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 383-401. http://geodesic.mathdoc.fr/item/CMUC_1994__35_2_a19/