On the cardinality and weight spectra of compact spaces, II
Logic
2009-09-25 v1 General Topology
Abstract
Let B(kappa, lambda) be the subalgebra of P(kappa) generated by [kappa]^{<= lambda}. It is shown that if B is any homomorphic image of B(kappa, lambda) then either |B|< 2^lambda or |B|=|B|^lambda, moreover if X is the Stone space of B then either |X| <= 2^{2^lambda} or |X|=|B|=|B|^lambda. This implies the existence of 0-dimensional compact T_2 spaces whose cardinality and weight spectra omit lots of singular cardinals of ``small'' cofinality.
Cite
@article{arxiv.math/9703220,
title = {On the cardinality and weight spectra of compact spaces, II},
author = {Istvan Juhász and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9703220},
year = {2009}
}