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

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

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

Every metric space is both second countable and separable.

Second countability and separability are equivalent for metric spaces.

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