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:
“A masterpiece is ... something said once and for all, stated, finished, so that it’s there complete in the mind, if only at the back.”
—Virginia Woolf (1882–1941)
“When my body leaves me
I’m lonesome for it.
but body
goes away to I don’t know where
and it’s lonesome to drift
above the space it
fills when it’s here.”
—Denise Levertov (b. 1923)