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Topology

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Moderate

Metric Spaces and Countability

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Which of the following best summarizes the relationship between metric spaces, second countability, and separability?

A

Every metric space is separable, but not necessarily second countable.

B

Every metric space is second countable, but not necessarily separable.

C

Every metric space is both second countable and separable.

D

Second countability and separability are equivalent for metric spaces.

E

Every topological space that is second countable and separable has a topology arising from some metric.