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The Nagata–Smirnov metrization theorem in topology characterizes when a topological space is metrizable. The theorem states that a topological space is metrizable if and only if it is regular, Hausdorff and has a countably locally finite (i.e., σ-locally finite) basis. A topological space X is called a regular space if every non-empty closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods. A collection in a space X is countably locally finite (or σ-locally finite) if it is the union of a countable family of locally finite collections of subsets of X. Unlike Urysohn's metrization theorem, which provides only a sufficient condition for metrizability, this theorem provides both a necessary and sufficient condition for a topological space to be metrizable. The theorem is named after Junichi Nagata and Yuriĭ Mikhaĭlovich Smirnov. ==See also== *Bing metrization theorem 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Nagata–Smirnov metrization theorem」の詳細全文を読む スポンサード リンク
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