1. The problem statement, all variables and given/known data Can a complete metric space have empty interior? 2. Relevant equations In mathematical analysis, a metric space M is said to be complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M. 3. The attempt at a solution But if M has no Cauchy sequence to start with or anything else for that matter (i.e have empty interior than it can also be labeled as complete? Or is my understanding lacking some important information?