\(\pi\)-weight and the Fréchet-Urysohn property (Q2252596)

A topological space for which sequential closure is the same as topological closure is called Fréchet-Urysohn. Several mathematicians have asked about the spectrum of cardinals \(\kappa\) for which there is a countable regular Fréchet-Uryshon space with \(\pi\)-weight \(\kappa\). The author shows there is a countable Fréchet-Urysohn space with \(\pi\)-weight at least \(b\), where \(b\) is a cardinal invariant called bounding number. The question ``Is there a countable Fréchet-Urysohn space with \(\pi\)-weight equal to \(b\)?'' remains open.