## A tall space with a small bottom

**István Juhász, Saharon Shelah, Lajos Soukup and
Zoltán Szentmiklóssy**

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
then there is such a space of
height with only many isolated points. This implies
that there is a locally compact scattered space
of height
with
isolated points in ZFC, solving an old problem
of the first author.

**Key words and phrases**: locally compact scattered space, superatomic Boolean algebra

**2000 Mathematics Subject Classification**: 54A25, 06E05, 54G12, 03E20

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