complete metric space

A complete metric space is a set of points where the concept of distance (defined by a metric) is used to measure how close points are to each other. In such a space, any sequence of points that gets closer and closer to some limit (called a Cauchy sequence) will always actually reach a point within the space that it approaches. This means there are no "gaps" or missing points where sequences could "converge" but not find their limit within the set. Completeness ensures that the space is "full" with respect to limits of converging sequences.