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Metric spaces and the axiom of choice

✍ Scribed by Omar De la Cruz; Eric Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin

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

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✦ Synopsis

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.

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Consequences of the failure of the axiom
Consequences of the failure of the axiom of choice in the theory of Lindelöf metric spaces
✍ 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