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
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
Journal title :
Topology and its Applications