Elementary chains and compact spaces with a small diagonal

Details Elementary chains and compact spaces with a small diagonal Elementary chains and compact spaces with a small diagonal

2011-09-08

arxiv.org/abs/1109.1736v1

Mathematics

General Topology

Scientific paper

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.

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