A tall space with a small bottom

Juhász, István; Shelah, Saharon; Soukup, Lajos; Szentmiklóssy, Zoltán

doi:10.1090/S0002-9939-03-06662-0

A tall space with a small bottom
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by István Juhász, Saharon Shelah, Lajos Soukup and Zoltán Szentmiklóssy PDF

Proc. Amer. Math. Soc. 131 (2003), 1907-1916 Request permission

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 ${\omega }_2$ with $\omega _1$ isolated points in ZFC, solving an old problem of the first author.

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