Continuing horrors of topology without choice

I. J. Tree*, Christopher Good

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


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 Urysohn's Metrization Theorem is entirely effective, whilst recalling that some choice is required for Urysohn's 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.

Original languageEnglish
Pages (from-to)79-90
Number of pages12
JournalTopology and its Applications
Issue number1
Publication statusPublished - 21 Apr 1995


  • Axiom of Choice
  • Suslin line
  • Urysohn's Lemma
  • Urysohn's Metrization Theorem
  • ω

ASJC Scopus subject areas

  • Geometry and Topology


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