## Abstract We show that the Axiom of Choice is equivalent to each of the following statements: (i) A product of closures of subsets of topological spaces is equal to the closure of their product (in the product topology); (ii) A product of complete uniform spaces is complete.
β¦ LIBER β¦
An Equivalence-Theoretic Equivalent of the Axiom of Choice
β Scribed by M. Armbrust
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 84 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
TWO TOPOLOGICAL EQUIVALENTS OF THE AXIOM
β
Eric Schechter; E. Schechter
π
Article
π
1992
π
John Wiley and Sons
π
English
β 159 KB
π 1 views
On some Theorems Equivalent with the Axi
β
Bernhard Banaschewski
π
Article
π
1961
π
John Wiley and Sons
π
English
β 251 KB
π 1 views
The Vector Space Kinna-Wagner Principle
β
Kyriakos Keremedis
π
Article
π
2001
π
John Wiley and Sons
π
English
β 129 KB
π 2 views
Lattice Theoretical Equivalences of the
β
Yehuda Rav
π
Article
π
1989
π
John Wiley and Sons
π
English
β 428 KB
The Induction Axiom and the Axiom of Cho
β
B. Germansky
π
Article
π
1961
π
John Wiley and Sons
π
English
β 326 KB
π 1 views
Unions and the axiom of choice
β
Omar De la Cruz; Eric J. Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin
π
Article
π
2008
π
John Wiley and Sons
π
English
β 176 KB
π 1 views
## Abstract We study statements about countable and wellβordered unions and their relation to each other and to countable and wellβordered forms of the axiom of choice. Using WO as an abbreviation for βwellβorderableβ, here are two typical results: The assertion that every WO family of countable se