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    Can Every Compact Metric Space Have a Countable Base?

    Rudin distinguishes finite sets and countable sets in his book. Would this affect the validity of the statement?
  2. I

    Can Every Compact Metric Space Have a Countable Base?

    Rudin's problem asks: Prove that every compact metric space K has a countable base. My concern is how valid this statement really is. Wouldn't a finite compact metric space be unable to have a countable base?
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