On Lindelof Metric Spaces and Weak Forms of the Axiom of Choice

Mathematical Logic Quarterly 46 (1):35-44 (2000)
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Abstract

We show that the countable axiom of choice CAC strictly implies the statements “Lindelöf metric spaces are second countable” “Lindelöf metric spaces are separable”. We also show that CAC is equivalent to the statement: “If is a Lindelöf topological space with respect to the base ℬ, then is Lindelöf”

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