The paper under review contains one single main theorem: if \(X\) is any Hausdorff space, and \(\kappa\) is the maximum of \(\hat{F}(X)\) (the minimum cardinal number such that every free subset of \(X\) has cardinality strictly smaller) and \(\hat{\mu}(X)\) (the minimum of all Lindelöf numbers of closures of free subsets of \(X\)), then for every cardinal number \(\varrho\) satisfying \(\varrho^{<\kappa}=\varrho\) we have \(L(X_{<\kappa})\leq\varrho\). Here \(X_{<\kappa}\) denotes the \(<\kappa\)-modification of \(X\), namely the topological space with the same underlying set as \(X\) and with the topology generated by intersections of less than \(\kappa\) open subsets of \(X\) (so that, in particular, with \(\kappa=\omega_1\) we recover the \(G_\delta\)-modification of \(X\)), and a set \(S\subseteq X\) is said to be free if it admits an indexing by ordinals, \(S=\{x_\alpha \mid \alpha<\lambda\}\) such that for all \(\alpha<\lambda\) the closures of \(\{x_\xi \mid \xi<\alpha\}\) and of \(\{x_\xi \mid \xi\geq\alpha\}\) are disjoint.
After stating this result and briefly analyzing the kinds of cardinal numbers \(\varrho\) to which the previous theorem might apply, the authors explain how a particular case of the previous result yields, assuming \(2^{<\mathfrak c}=\mathfrak c\), an affirmative answer to a question of A. Bella (whether any linearly Lindelöf regular space of countable tightness satisfies that, in its \(G_\delta\)-modification, every set of regular cardinality strictly larger than \(\mathfrak c\) has a complete accumulation point) that reached the authors of the paper under review through a personal communication.