Elementary chains and compact spaces with a small diagonal

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2 Citations (Scopus)

Abstract

It is a well known open problem if, in View the MathML sourceZFC, 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.
Original languageEnglish
Pages (from-to)438-447
Number of pages10
JournalIndagationes Mathematicae
Volume23
Issue number3
DOIs
Publication statusPublished - 2012

Keywords

  • Small diagonal
  • Metrizable
  • Chains of elementary substructures

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