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# A Tall Space with a Small Bottom

István Juhász, Saharon Shelah, Lajos Soukup and Zoltán Szentmiklóssy
Proceedings of the American Mathematical Society
Vol. 131, No. 6 (Jun., 2003), pp. 1907-1916
Stable URL: http://www.jstor.org/stable/1194370
Page Count: 10
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## 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 κ + with only κ many isolated points. This implies that there is a locally compact scattered space of height ω 2 with ω 1 isolated points in ZFC, solving an old problem of the first author.

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