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The failure of the axiom of choice implies unrest in the theory of Lindelöf metric spaces

✍ Scribed by Kyriakos Keremedis


Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
156 KB
Volume
49
Category
Article
ISSN
0044-3050

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✦ Synopsis


Abstract

In the realm of metric spaces the role of choice principles is investigated.


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Consequences of the failure of the axiom
✍ Kyriakos Keremedis 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 167 KB

## Abstract We study within the framework of Zermelo‐Fraenkel set theory ZF the role that the axiom of choice plays in the theory of Lindelöf metric spaces. We show that in ZF the weak choice principles: (i) Every Lindelöf metric space is separable and (ii) Every Lindelöf metric space is second cou

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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.