Elementary chains and compact spaces with a small diagonal
type: Item
instance of: scholarly article
title: Elementary chains and compact spaces with a small diagonal
zbMATH Open document ID: 1248.54014
author: Alan Dow
author: K. P. Hart
published in: Indagationes Mathematicae. New Series
publication date: 2012-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.1736
review text: A~space~\(X\) is said to have a~small diagonal, if every uncountable subset of~\(X^2\) that is disjoint from the diagonal has an uncountable subset whose closure is disjoint from the diagonal. By a~csD-space is meant a~compact Hausdorff space with a~small diagonal. The authors explore properties of csD-spaces using elementary chains of substructures. They prove that ccc subspaces of csD-spaces have countable \(\pi\)-weight, they generalize a~result of Gruenhage about spaces which are metrizably fibered, and they prove that if there is a~Luzin set of reals, then every csD-space has many points of countable character. The main question on csD-spaces, namely whether they are metrizable, remains open.
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54D70
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 6070494
zbMATH Keywords: small diagonal
zbMATH Keywords: metrizable
zbMATH Keywords: chains of elementary substructures
MaRDI profile type: Publication
OpenAlex ID: W3102115506
arXiv ID: 1109.1736
cites work: More about spaces with a small diagonal
cites work: Analytic quotients: theory of liftings for quotients over analytic ideals on the integers
cites work: Spaces having a small diagonal
cites work: Q4151370
cites work: Convergent Free Sequences in Compact Spaces
cites work: Set theory.
cites work: Q4870679
cites work: On the small diagonals
DOI: 10.1016/J.INDAG.2012.02.008
description: scientific article; zbMATH DE number 6070494