Sequentially linearly Lindelöf spaces

Menachem Kojman, Victoria Lubitch

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A topological Hausdorff space X is sequentially linearly Lindelöf if for every uncountable regular cardinal κ≤w(X) and every A⊆X of cardinality κ there exists B⊆A of cardinality κ which converges to a point. We prove that the existence of a good (μ,λ)-scale for a singular cardinal μ of countable cofinality and a regular λ>μ implies the existence of a sequentially linearly Lindelöf space of cardinality λ and weight μ which is not Lindelöf.Corollaries of the main result are: (1) it is consistent to have linearly Lindelöf non-Lindelöf spaces below the continuum; (2) it is consistent to have a realcompact linearly Lindelöf non-Lindelöf space below 2אω; (3) it is consistent to have a Dowker topology on אω+1 in which every subset of cardinality אn, n>0, has a converging subset of the same cardinality; (4) the nonexistence of sequentially linearly Lindelöf non-Lindelöf spaces implies the consistency of large cardinals.

Original languageEnglish
Pages (from-to)135-144
Number of pages10
JournalTopology and its Applications
Issue number2-3
StatePublished - 15 Feb 2003


  • Complete accumulation
  • Inner models
  • Large cardinals
  • Linearly Lindelöf spaces
  • PCF-theory
  • Realcompact spaces
  • Singular cardinals
  • Square principle

ASJC Scopus subject areas

  • Geometry and Topology


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