High Quality Content by WIKIPEDIA articles! 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 or alternatively if every Cauchy sequence in M converges in M.Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).Thus, a complete metric space is analogous to a closed set. It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.

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