A tall space with small bottom
Istvan Juhász, Saharon Shelah, Lajos Soukup, Zoltan Szentmiklóssy
Abstract
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 omega2 with omega1 isolated points in ZFC, solving an old problem of the first author.
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