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A tall space with small bottom

Istvan Juhász·Saharon Shelah·Lajos Soukup·Zoltan Szentmiklóssy
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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 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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Istvan Juhász, Saharon Shelah, Lajos Soukup, Zoltan Szentmiklóssy. 2001-04-19. A tall space with small bottom. https://arxiv.org/abs/math/0104198

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