The Axiom of Countable Choice and Pointfree Topology
β Scribed by Bernhard Banaschewski
- Book ID
- 110299393
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 113 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0927-2852
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## 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.
## Abstract It is easy to prove in ZF^β^ (= ZermeloβFraenkel set theory without the axioms of choice and foundation) that a relation __R__ satisfies the maximal condition if and only if its transitive hull __R__\* does; equivalently: __R__ is wellβfounded if and only if __R__\* is. We will show in