Countable choice and compactness
โ Scribed by Marianne Morillon
- Book ID
- 108286476
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 180 KB
- Volume
- 155
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We show that it is consistent with the Continuum Hypothesis that first countable, countably compact spaces with no uncountable free sequences are compact. As a consequence, we get that CH does not imply the existence of a perfectly normal, countably compact, non-compact space, answering a question o
In the realm of pseudometric spaces the role of choice principles is investigated. In particular it is shown that in ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the axiom of countable choice is not only sufficient but also necessary to establish each of the following results: