Abstract
The main result of this note is the following theorem.If X is any Hausdorff space withκ=Fˆ(X)⋅μˆ(X)thenL(X<κ)≤ϱ(κ).Here Fˆ(X) is the smallest cardinal φ so that |S|<φ for any set S that is free in X and μˆ(X) is the smallest cardinal μ so that, for every set S that is free in X, any open cover of S‾ has a subcover of size <μ. Moreover, X<κ is the G<κ-modification of X and ϱ(κ)=min{ϱ:ϱ<κ=ϱ}.As a corollary we obtain that if X is a linearly Lindelöf regular space of countable tightness then L(Xδ)≤c, provided that c=2<c. This yields a consistent affirmative answer to a question of Angelo Bella.
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