A tall space with a small bottom

by Juhasz and Shelah and Soukup and Szentmiklossy. [JShSS:714]
Proc American Math Soc, 2003
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.


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