Matches in DBpedia 2016-04 for { ?s ?p "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. √2 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."@en }
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- Complete_metric_space abstract "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. √2 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.".