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

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”
Keywords Lindelöf space  Pseudometrice space  Countable axiom of choice
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DOI 10.1002/(sici)1521-3870(200001)46:1
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