A tall space with small bottom

Juhász, Istvan; Shelah, Saharon; Soukup, Lajos; Szentmiklóssy, Zoltan

A tall space with small bottom

Authors

Juhász, Istvan

Shelah, Saharon

Soukup, Lajos

Szentmiklóssy, Zoltan

Description

We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if kappa^{<kappa}=kappa then there is such a space of height kappa^+ with only kappa many isolated points. This implies that there is a locally compact scattered space of height omega_2 with omega_1 isolated points in ZFC, solving an old problem of the first author.