analysis functional-analysis metric-spaces
Definition
Completeness
A mathematical structure is complete if every Cauchy sequence in it converges to a limit that is also in the structure.
Metric spaces
For a metric space, this means that no limit point is missing from the space. A complete metric space is a complete metric space.
Normed vector spaces
A normed vector space is complete exactly when it is a Banach space.
Real numbers
The real numbers are complete in the sense of the completeness theorem of the real numbers.