Back فضاء كامل Arabic Espai complet Catalan Úplný metrický prostor Czech Fuldstændigt metrisk rum Danish Vollständiger Raum German Πλήρης μετρικός χώρος Greek Kompleta metrika spaco Esperanto Espacio métrico completo Spanish فضای متریک کامل Persian Täydellisyys Finnish
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.
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 further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, as explained below.
