### 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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