## 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.
Filters, Antichains and Towers in Topological Spaces and the Axiom of Choice
โ Scribed by Kyriakos Keremedis
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 463 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
โฆ Synopsis
We find some characterizations of the Axiom of Choice (AC) in terms of certain families of open sets in TI spaces.
๐ 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 This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces (first and second countable spaces, Hausdorff spaces, and subspaces of โ^__K__^). We also study well ordered Tychonoff products and the effect