Complete Metric Space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) 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). For instance, the set of rational numbers is not complete, because e.g. is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it. (See the examples below.) It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.
Read more about Complete Metric Space: Examples, Some Theorems, Completion, Topologically Complete Spaces, Alternatives and Generalizations
Famous quotes containing the words complete and/or space:
“Silence is to all creatures thus attacked the only means of salvation; it fatigues the Cossack charges of the envious, the enemy’s savage ruses; it results in a cruising and complete victory.”
—Honoré De Balzac (1799–1850)
“from above, thin squeaks of radio static,
The captured fume of space foams in our ears—”
—Hart Crane (1899–1932)