Continuing horrors of topology without choice
Topology and its ApplicationsPublished 1 April 1995
Chris Good, I.J. Tree
Citations85
SJR quartileQ2
SJR score0.45
SNIP0.83
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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 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.
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Computer ScienceMathematics
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