# 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. arXiv: math/0104198 DOI: 10.1090/S0002-9939-03-06662-0 MR: 1955280 -
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. - 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}, doi = {10.1090/S0002-9939-03-06662-0}, mrclass = {54A25 (03E20 54G12)}, mrnumber = {1955280}, mrreviewer = {Andrzej Szyma\'nski}, 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} }