An anti-Hausdorff Fréchet space in which convergent sequences have unique limits (Q689602)

The author's introduction: ``We answer an old question of Novák by constructing an anti-Hausdorff Fréchet space in which convergent sequences have unique limits. An essential ingredient in our construction is that there exists an infinite maximal almost disjoint family \({\mathcal A}\) on \(\omega\) and a function \(L:{\mathcal A}\to\omega\) such that for all \(X \subseteq \omega\), if \({\mathcal F}=\{A \in{\mathcal A}:| A \cap X |= \omega \}\) is infinite then \(L^ \to {\mathcal F}=\omega\). We also discuss possible strengthenings and generalizations of this result.