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The sequentiality is equivalent to the \({\mathcal F}\)-Fréchet-Urysohn property. (English) Zbl 0696.54020
Some relations between sequentiality, \({\mathcal F}\)-Fréchet-Urysohn property and \({\mathcal F}\)-sequentiality are shown. Theorem 1. There exists a filter \({\mathcal F}\) on \(\omega\) such that every Hausdorff sequential space is \({\mathcal F}\)-Fréchet-Urysohn. Example 1, [CH]. For every ultrafilter p on \(\omega\) which is a P-point on \(\omega^*\) there exists a compact Franklin’s space whose index of p-sequentiality equals 2. Example 2, [CH]. There exists a sequential compact space which is p- Fréchet-Urysohn for no P-point \(p\in \omega^*\). Theorem 2. Every compact Franklin’s space is p-Fréchet-Urysohn for no P-point \(p\in \omega^*\).

54D55 Sequential spaces
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54A35 Consistency and independence results in general topology
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