Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673021 | Indagationes Mathematicae | 2012 | 10 Pages |
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 substructures. We prove that ccc subspaces of such spaces have countable ππ-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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Alan Dow, Klaas Pieter Hart,