Abstract:We present a forcing construction of a Hausdorff zero-dimensional Lindel\"of space $X$ whose square $X^2$ is again Lindel\"of but its cube $X^3$ has a closed discrete subspace of size ${\frak c}^+$, hence the Lindel\"of degree $L(X^3) = {\frak c}^+ $. In our model the Continuum Hypothesis holds true. \par 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 $L(X^{\aleph _0}) = {\frak c}^+ = \aleph _2$.
Keywords: forcing, topology, products, Lindel\"of
AMS Subject Classification: 54D20,54B10, 03E35