# Sh:714

• Juhász, I., Shelah, S., Soukup, L., & Szentmiklóssy, Z. (2003). A tall space with a small bottom. Proc. Amer. Math. Soc., 131(6), 1907–1916.
• 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.
• Version 2001-04-02_11 (10p) published version (10p)
Bib entry
@article{Sh:714,
author = {Juh{\'a}sz, Istv{\'a}n and Shelah, Saharon and Soukup, Lajos and Szentmikl{\'o}ssy, Zolt{\'a}n},
title = {{A tall space with a small bottom}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {131},
number = {6},
year = {2003},
pages = {1907--1916},
issn = {0002-9939},
mrnumber = {1955280},
mrclass = {54A25 (03E20 54G12)},
doi = {10.1090/S0002-9939-03-06662-0},
note = {\href{https://arxiv.org/abs/math/0104198}{arXiv: math/0104198}},
arxiv_number = {math/0104198},
keyword = {Locally compact scattered space, superatomic Boolean algebra}
}