Three-space properties of some kinds of coset spaces (Q6592028)

A three-space property is a topological property, say \(P\), that satisfies the following: let \(G\) be a topological group with closed subgroups \(H\) and \(K\) such that \(H\subseteq K\), then: if the coset spaces \(G/K\) and \(K/H\) have property \(P\) then so does \(G/H\).\N\NThe authors investigate a sizable number of properties in this context, ranging from the Fréchet-Urysohn property (and variations) via the existence of a certain type of networks (cosmic, \(\aleph_0\)-, \(\sigma\)-spaces, and more) to other generalized metrizable spaces, such as (semi-) stratifiability. The results do not always identify three-space properties exactly, they generally identify extra assumptions that need to be made on some of the quotients for the desired implication to hold.