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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 sub-space of size c + , hence the Lindelöf degree L(X 3) = 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) =(More)
A topological space X is called weakly first countable, if for every point x there is a countable family {C x n | n ∈ ω} such that x ∈ C x n+1 ⊆ C x n and such that U ⊂ X is open iff for each x ∈ U some C x n is contained in U. This weakening of first count-ability is due to A. V. Arhangelskii from 1966, who asked whether compact weakly first countable(More)
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