The cardinality of compact spaces satisfying the countable chain condition

Research output: Contribution to journalArticle

Abstract

We prove that for a compact Hausdorff space X, if λc(X)<w(X) for every infinite cardinal λ<w(X) and λc(X)<cf(w(X)) for every infinite cardinal λ<cf(w(X)), then Tikhonov cube [0,1]w(X) is a continuous image of X, in particular the cardinality of X is just 2w(X). As an application of this result, we consider elementary submodel spaces and improve Tall's result in [17].

Original languageEnglish
Pages (from-to)41-55
Number of pages15
JournalTopology and its Applications
Volume174
DOIs
Publication statusPublished - 2014 Sep 1

Keywords

  • Compact space
  • Countable chain condition
  • Dyadic system
  • Elementary submodel space
  • Independent family
  • Precaliber

ASJC Scopus subject areas

  • Geometry and Topology

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