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A tall space with a small bottom |
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| Authors: | Istvá n Juhá sz Saharon Shelah Lajos Soukup Zoltá n Szentmikló ssy |
| Affiliation: | Alfréd Rényi Institute of Mathematics, P.O. Box 127, 1364 Budapest, Hungary ; Institute of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel ; Alfréd Rényi Institute of Mathematics, P.O. Box 127, Budapest, Hungary ; Eötvös University of Budapest, 1117, Budapest, Pázmány Péter Sétány 1/C, Hungary |
| 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  , 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. |
| Keywords: | Locally compact scattered space superatomic Boolean algebra |
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