𝑝-sequentiality and 𝑝-Fréchet-Urysohn property of Franklin compact spaces

Abstract

Franklin compact spaces defined by maximal almost disjoint families of subsets of ω \omega are considered from the view of its p p -sequentiality and p p -Fréchet-Urysohn-property for ultrafilters p ∈ ω ∗ p\in \omega ^* . Our principal results are the following: CH implies that for every P P -point p ∈ ω ∗ p\in \omega ^* there are a Franklin compact p p -Fréchet-Urysohn space and a Franklin compact space which is not p p -Fréchet-Urysohn; and, assuming CH, for every Franklin compact space there is a P P -point q ∈ ω ∗ q\in \omega ^* such that it is not q q -Fréchet-Urysohn. Some new problems are raised.