Elementary chains and compact spaces with a small diagonal
General Topology
2012-07-25 v1 Logic
Abstract
It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of submodels. We prove that ccc subspaces of such spaces have countable \pi-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set of reals, then every compact space with a small diagonal will have many points of countable character.
Cite
@article{arxiv.1109.1736,
title = {Elementary chains and compact spaces with a small diagonal},
author = {Alan Dow and Klaas Pieter Hart},
journal= {arXiv preprint arXiv:1109.1736},
year = {2012}
}