At the beginning of the 1970s, M. Katětov discovered that iterated Fubini products of the Fréchet filter play a crucial role in the theory of Baire classes of functions.
Recently, it has been shown that the transfinitely iterated Fréchet ideals are critical for maximal almost disjoint families or Ellentuck spaces. We show that these ideals fit well with the specific hierarchy of topological spaces related to delta-sets. Consequently, we get a solution to two problems on the Fréchet-Urysohn property of function spaces.
This is a joint work with S. Bardyla and L. Zdomskyy.