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
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