Is every compact metric space meets the second countable?
Do you may have a condition equivalent? I miss just this one proof and ask for help.
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1Every compact metric spaceis the second countable. For a proof: http://planetmath.org/sites/default/files/texpdf/39296.pdf – Fred Feb 17 '17 at 12:08
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For metric spaces, the properties of being second-countable, separable, and Lindelöf are all equivalent: similar question – Simon Marynissen Feb 17 '17 at 13:08