• Title of article

    Continuing horrors of topology without choice

  • Author/Authors

    Good، نويسنده , , C. and Tree، نويسنده , , I.J.، نويسنده ,

  • Issue Information
    دوماهنامه با شماره پیاپی سال 1995
  • Pages
    12
  • From page
    79
  • To page
    90
  • Abstract
    Various topological results are examined in models of Zermelo-Fraenkel set theory that do not satisfy the Axiom of Choice. In particular, it is shown that the proof of Urysohnʹs Metrization Theorem is entirely effective, whilst recalling that some choice is required for Urysohnʹs Lemma. R is paracompact and ω1 may be paracompact but never metrizable. An example of a nonmetrizable paracompact manifold is given. Suslin lines, normality of LOTS and consequences of Countable Choice are also discussed.
  • Keywords
    Suslin line , Urysohnיs Lemma , AXIOM OF CHOICE , ?1 , Urysohnיs Metrization Theorem
  • Journal title
    Topology and its Applications
  • Serial Year
    1995
  • Journal title
    Topology and its Applications
  • Record number

    1578615