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In topology, a discipline within mathematics, an Urysohn space, or T2½ space, is a topological space in which any two distinct points can be separated by closed neighborhoods. A completely Hausdorff space, or functionally Hausdorff space, is a topological space in which any two distinct points can be separated by a continuous function. These conditions are separation axioms that are somewhat stronger than the more familiar Hausdorff axiom T2. ==Definitions== Suppose that ''X'' is a topological space. Let ''x'' and ''y'' be points in ''X''. *We say that ''x'' and ''y'' can be ''separated by closed neighborhoods'' if there exists a closed neighborhood ''U'' of ''x'' and a closed neighborhood ''V'' of ''y'' such that ''U'' and ''V'' are disjoint (''U'' ∩ ''V'' = ∅). (Note that a "closed neighborhood of ''x''" is a closed set that contains an open set containing ''x''.) *We say that ''x'' and ''y'' can be ''separated by a function'' if there exists a continuous function ''f'' : ''X'' → () (the unit interval) with ''f''(''x'') = 0 and ''f''(''y'') = 1. A Urysohn space, or T2½ space, is a space in which any two distinct points can be separated by closed neighborhoods. A completely Hausdorff space, or functionally Hausdorff space, is a space in which any two distinct points can be separated by a continuous function. 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「Urysohn and completely Hausdorff spaces」の詳細全文を読む スポンサード リンク
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