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On the Axiom of Choice and the Continuum Hypothesis

✍ Scribed by Rolf Schock


Publisher
John Wiley and Sons
Year
1971
Tongue
English
Weight
162 KB
Volume
17
Category
Article
ISSN
0044-3050

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πŸ“œ SIMILAR VOLUMES


Unions and the axiom of choice
✍ Omar De la Cruz; Eric J. Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 176 KB πŸ‘ 1 views

## Abstract We study statements about countable and well‐ordered unions and their relation to each other and to countable and well‐ordered forms of the axiom of choice. Using WO as an abbreviation for β€œwell‐orderable”, here are two typical results: The assertion that every WO family of countable se

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## Abstract We study conditions for a topological space to be metrizable, properties of metrizable spaces, and the role the axiom of choice plays in these matters.

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We show that for every well ordered cardinal number m the Tychonoff product 2 m is a compact space without the use of any choice but in Cohen's Second Model 2 R is not compact.