CONTINUING HORRORS OF TOPOLOGY WITHOUT CHOICE
| Autor: | I. J. Tree, Chris Good |
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| Předmět: |
Discrete mathematics
Lemma (mathematics) Urysohn's Metrization Theorem Mathematics::General Topology Suslin line Topology Axiom of Choice Urysohn's Lemma Urysohn's lemma Mathematics::Logic ω1 Metrization theorem Choice function Countable set Axiom of choice Paracompact space Set theory Geometry and Topology Mathematics |
| Zdroj: | ResearcherID |
| Popis: | 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 ω 1 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. |
| Databáze: | OpenAIRE |
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