A tall space with small bottom
Logic
2007-05-23 v1 General Topology
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.
Keywords
Cite
@article{arxiv.math/0104198,
title = {A tall space with small bottom},
author = {Istvan Juhász and Saharon Shelah and Lajos Soukup and Zoltan Szentmiklóssy},
journal= {arXiv preprint arXiv:math/0104198},
year = {2007}
}