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For metric spaces, second-countability, separability, and the Lindelöf property are all equivalent.
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Other examples of mathematical objects obeying axioms of countability include
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Every second-countable space is first countable, separable, and Lindelöf.
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These axioms are related to each other in the following ways:
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121:: there exists a countable cover by compact spaces
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134:Every first-countable space is sequential.
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194:Modern General Topology
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