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The sequentiality and the Fréchet-Urysohn property with respect to ultrafilters. (English) Zbl 0792.54024

The author proves that some propositions are consistent with ZFC, e.g.
1. A space is ultrasequential iff it is sequential.
2. There exists \(p \in \omega^*\) such that corresponding Arens space is not \(p\)-sequential.
3. Every Arens space is an ultra-Fréchet space.

MSC:

54D55 Sequential spaces
54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.)
54A35 Consistency and independence results in general topology
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