## Abstract Under the axiom of choice, every first countable space is a Fréchet‐Urysohn space. Although, in its absence even ℝ may fail to be a sequential space. Our goal in this paper is to discuss under which set‐theoretic conditions some topological classes, such as the first countable spaces,
✦ LIBER ✦
On the contrapositive of countable choice
✍ Scribed by Hajime Ishihara; Peter Schuster
- Book ID
- 105842414
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 130 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0933-5846
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## Abstract It is easy to prove in ZF^−^ (= Zermelo‐Fraenkel 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 well‐founded if and only if __R__\* is. We will show in