[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ12 (1002ﾚｽ)
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552: 現代数学の系譜 雑談 ◆yH25M02vWFhP 01/23(木)21:02 ID:y/IThbaj(3/6) AA×

外部ﾘﾝｸ:en.wikipedia.org

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552: 現代数学の系譜 雑談 ◆yH25M02vWFhP [] 2025/01/23(木) 21:02:41.63 ID:y/IThbaj つづき https://en.wikipedia.org/wiki/Complete_metric_space 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. 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 further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, as explained below. (引用終り) 以上 http://rio2016.5ch.net/test/read.cgi/math/1735693028/552
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