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:
“As a wicked man I am a complete failure. Why, there are lots of people who say I have never really done anything wrong in the whole course of my life. Of course they only say it behind my back.”
—Oscar Wilde (1854–1900)
“Time in his little cinema of the heart
Giving a première to Hate and Pain;
And Space urbanely keeping us apart.”
—Philip Larkin (1922–1986)