. "Espacio uniforme"@es . . . . . "Espace uniforme"@fr . "En math\u00E9matiques, la notion d'espace uniforme, introduite en 1937 par Andr\u00E9 Weil, est une g\u00E9n\u00E9ralisation de celle d'espace m\u00E9trique. Une structure uniforme est une structure qui permet de d\u00E9finir la continuit\u00E9 uniforme. On peut y parvenir de deux mani\u00E8res diff\u00E9rentes, l'une en g\u00E9n\u00E9ralisant la notion de distance, l'autre avec une axiomatique proche de celle des espaces topologiques. On montre que ces deux approches sont \u00E9quivalentes."@fr . . . . . . . . "In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure that is used to define uniform properties such as completeness, uniform continuity and uniform convergence. Uniform spaces generalize metric spaces and topological groups, but the concept is designed to formulate the weakest axioms needed for most proofs in analysis."@en . . "'uniform structure' links to here, so this term shouldn't be used in the definiens."@en . . . "Uniforme R\u00E4ume sind im Teilgebiet Topologie der Mathematik Verallgemeinerungen metrischer R\u00E4ume. Jeder metrische Raum kann auf nat\u00FCrliche Weise als uniformer Raum betrachtet werden, und jeder uniforme Raum kann auf nat\u00FCrliche Weise als topologischer Raum betrachtet werden. Ein uniformer Raum ist eine Menge mit einer sogenannten uniformen Struktur, die eine Topologie auf der Menge definiert, zus\u00E4tzlich aber erlaubt, Umgebungen an verschiedenen Punkten miteinander zu vergleichen und die aus der Theorie der metrischen R\u00E4ume bekannten Begriffe wie Vollst\u00E4ndigkeit, gleichm\u00E4\u00DFige Stetigkeit und gleichm\u00E4\u00DFige Konvergenz zu verallgemeinern und zu abstrahieren. Das Konzept der uniformen R\u00E4ume gestattet die Formalisierung der Idee, dass \u201Eein Punkt gleich nah bei einem anderen Punkt ist, wie ein dritter Punkt bei einem vierten Punkt \u201C, w\u00E4hrend in topologischen R\u00E4umen nur Aussagen der Form \u201E ist gleich nah bei wie bei ist\u201C gemacht werden k\u00F6nnen. Anders als bei metrischen R\u00E4umen wird dieser Vergleich hier nicht durch ein Abstandsma\u00DF vermittelt, sondern durch eine direkte Beziehung zwischen den Umgebungsfiltern von und . Neben metrischen R\u00E4umen induzieren auch topologische Gruppen uniforme Strukturen auf der unterliegenden Menge. Ein topologischer Raum, zu dessen Topologie es eine uniforme Struktur gibt, die jene induziert, hei\u00DFt uniformisierbarer Raum. Dieser Begriff ist \u00E4quivalent zu dem des vollst\u00E4ndig regul\u00E4ren Raumes."@de . . . . . . "\u5728\u62D3\u6251\u5B66\u9019\u500B\u6578\u5B78\u9818\u57DF\u88E1\uFF0C\u4E00\u81F4\u7A7A\u95F4\uFF08uniform space\uFF09\u662F\u6307\u5E26\u6709\u4E00\u81F4\u7ED3\u6784\u7684\u96C6\u5408\u3002\u4E00\u81F4\u7A7A\u95F4\u662F\u4E00\u500B\u62D3\u64B2\u7A7A\u9593\uFF0C\u6709\u53EF\u4EE5\u7528\u6765\u5B9A\u4E49\u5982\u5B8C\u5907\u6027\u3001\u4E00\u81F4\u8FDE\u7EED\u53CA\u4E00\u81F4\u6536\u655B\u7B49\u4E00\u81F4\u6027\u8CEA\u7684\u9644\u52A0\u7ED3\u6784\u3002 \u4E00\u81F4\u7ED3\u6784\u548C\u62D3\u6251\u7ED3\u6784\u4E4B\u95F4\u7684\u6982\u5FF5\u533A\u522B\u5728\u65BC\uFF0C\u4E00\u81F4\u7A7A\u95F4\u53EF\u4EE5\u5F62\u5F0F\u5316\u6709\u5173\u4E8E\u76F8\u5BF9\u90BB\u8FD1\u6027\u53CA\u70B9\u95F4\u4E34\u8FD1\u6027\u7B49\u7279\u5B9A\u6982\u5FF5\u3002\u6362\u53E5\u8BDD\u8BF4\uFF0C\u300Cx \u90BB\u8FD1\u4E8Ea \u80DC\u8FC7y \u90BB\u8FD1\u4E8Eb\u300D\u4E4B\u985E\u7684\u6982\u5FF5\uFF0C\u5728\u4E00\u81F4\u7A7A\u95F4\u4E2D\u662F\u6709\u610F\u4E49\u7684\u3002\u800C\u76F8\u5BF9\u7684\uFF0C\u5728\u4E00\u822C\u62D3\u6251\u7A7A\u95F4\u5185\uFF0C\u7ED9\u5B9A\u96C6\u5408A \u548CB\uFF0C\u6709\u610F\u4E49\u7684\u6982\u5FF5\u53EA\u6709\uFF1A\u70B9x \u80FD\u201C\u4EFB\u610F\u90BB\u8FD1\u201DA\uFF08\u4EA6\u5373\u5728A \u7684\u95ED\u5305\u5167\uFF09\uFF1B\u6216\u662F\u548CB\u76F8\u6BD4\uFF0CA \u662Fx \u7684\u201C\u8F03\u5C0F\u90BB\u57DF\u201D\uFF0C\u4F46\u70B9\u95F4\u90BB\u8FD1\u6027\u548C\u76F8\u5BF9\u90BB\u8FD1\u6027\u5C31\u4E0D\u80FD\u53EA\u7528\u62D3\u6251\u7ED3\u6784\u4F86\u63CF\u8FF0\u4E86\u3002 \u4E00\u81F4\u7A7A\u95F4\u5E7F\u7FA9\u5316\u4E86\u5EA6\u91CF\u7A7A\u95F4\u548C\u62D3\u6251\u7FA4\uFF0C\u56E0\u6B64\u6210\u70BA\u591A\u6570\u6570\u5B66\u5206\u6790\u7684\u6839\u57FA\u3002"@zh . . . . "\u4E00\u69D8\u7A7A\u9593\uFF08\u3044\u3061\u3088\u3046\u304F\u3046\u304B\u3093\u3001\u82F1: uniform space\uFF09\u3068\u306F\u3001\u4E00\u69D8\u69CB\u9020\u3068\u3044\u3046\u69CB\u9020\u3092\u5099\u3048\u305F\u96C6\u5408\u3067\u3042\u308B\u3002\u4E00\u69D8\u69CB\u9020\u306F\u64EC\u8DDD\u96E2\u69CB\u9020\u3068\u4F4D\u76F8\u69CB\u9020\u306E\u4E2D\u9593\u306E\u5F37\u3055\u3092\u6301\u3061\u3001\u4F4D\u76F8\u69CB\u9020\u3060\u3051\u3067\u306F\u5B9A\u7FA9\u3067\u304D\u306A\u3044\u4E00\u69D8\u9023\u7D9A\u6027\u3001\u30B3\u30FC\u30B7\u30FC\u5217\u3001\u5B8C\u5099\u6027\u3001\u4E00\u69D8\u9023\u7D9A\u6027\u3001\u4E00\u69D8\u6709\u754C\u6027\u3001\u5168\u6709\u754C\u6027\u306A\u3069\u304C\u5B9A\u7FA9\u3067\u304D\u308B\u3002 \u307E\u305F\u64EC\u8DDD\u96E2\u7A7A\u9593\u306E\u307F\u306A\u3089\u305A\u4F4D\u76F8\u7FA4\uFF08\u3068\u304F\u306B\u4F4D\u76F8\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593\uFF09\u306B\u95A2\u3057\u3066\u3082\u81EA\u7136\u306A\u4E00\u69D8\u69CB\u9020\u304C\u5B9A\u307E\u308B\u4E8B\u304C\u77E5\u3089\u308C\u3066\u3044\u308B\u70BA\u3001\u4E00\u69D8\u7A7A\u9593\u306E\u6982\u5FF5\u306F\u95A2\u6570\u89E3\u6790\u5B66\u306B\u304A\u3044\u3066\u6709\u76CA\u3067\u3042\u308B\u3002 \u4F4D\u76F8\u7A7A\u9593\u3068\u306E\u9055\u3044\u306F\u3001\u4F4D\u76F8\u7A7A\u9593\u304C\u53CE\u675F\u6027\u3001\u3059\u306A\u308F\u3061\u70B9\u306B\u300C\u8FD1\u3065\u304F\u300D\u4E8B\u3092\u5B9A\u7FA9\u53EF\u80FD\u306A\u6982\u5FF5\u3067\u3042\u308B\u306E\u306B\u5BFE\u3057\u3001\u4E00\u69D8\u7A7A\u9593\u3067\u306F\u3042\u308B\u70B9\u304C\u5225\u306E\u70B9\u306B\u300C\u8FD1\u3044\u300D\u4E8B\u304C\u5B9A\u7FA9\u3067\u304D\u308B\u3002\u3057\u304B\u3057\u3053\u306E\u300C\u8FD1\u3055\u300D\u306F\u64EC\u8DDD\u96E2\u69CB\u9020\u306E\u3088\u3046\u306B\u5B9F\u6570\u5024\u3067\u5168\u9806\u5E8F\u3065\u3051\u3055\u308C\u3066\u304A\u3089\u305A\u3001\u8FD1\u7E01\u3068\u547C\u3070\u308C\u308B\u90E8\u5206\u96C6\u5408\u306B\u5C5E\u3059\u308B\u304B\u3069\u3046\u304B\u3067\u5224\u65AD\u3059\u308B\u534A\u9806\u5E8F\u7684\u306A\u3082\u306E\u3067\u3042\u308B\u3002"@ja . . . . . . . . "March 2020"@en . . "Uniforme R\u00E4ume sind im Teilgebiet Topologie der Mathematik Verallgemeinerungen metrischer R\u00E4ume. Jeder metrische Raum kann auf nat\u00FCrliche Weise als uniformer Raum betrachtet werden, und jeder uniforme Raum kann auf nat\u00FCrliche Weise als topologischer Raum betrachtet werden. Neben metrischen R\u00E4umen induzieren auch topologische Gruppen uniforme Strukturen auf der unterliegenden Menge. Ein topologischer Raum, zu dessen Topologie es eine uniforme Struktur gibt, die jene induziert, hei\u00DFt uniformisierbarer Raum. Dieser Begriff ist \u00E4quivalent zu dem des vollst\u00E4ndig regul\u00E4ren Raumes."@de . . "32339"^^ . . "In de topologie, een deelgebied van de wiskunde, is een uniforme ruimte een verzameling voorzien van een uniforme structuur (uniformiteit). Uniforme ruimten veralgemenen bepaalde eigenschappen en begrippen van metrische ruimten die weliswaar geen topologische invarianten zijn, maar die nauw verwant zijn met topologische eigenschappen, bijvoorbeeld Cauchyrijen en volledigheid, uniforme continu\u00EFteit en uniforme convergentie."@nl . . . . . . "\u4E00\u81F4\u7A7A\u95F4"@zh . . . . "Uniformer Raum"@de . "In topologia, uno spazio uniforme \u00E8 uno spazio topologico dotato di una struttura uniforme, che consente di definire propriet\u00E0 uniformi, come la completezza, la continuit\u00E0 uniforme e la convergenza uniforme. La struttura uniforme, e gli altri concetti ad essa collegati, fu definita esplicitamente da Andr\u00E9 Weil nel 1937, mediante l'utilizzo di pseudometriche. Successivamente Nicolas Bourbaki forn\u00EC la definizione in termini di entourage e John Tukey la diede in termini di ricoprimenti uniformi. Queste definizioni sono descritte nei paragrafi sottostanti."@it . "\uC77C\uBC18\uC704\uC0C1\uC218\uD559\uC5D0\uC11C \uADE0\uB4F1 \uACF5\uAC04(\u5747\u7B49\u7A7A\u9593, \uC601\uC5B4: uniform space)\uC740 \uB450 \uC810\uC774 \uC11C\uB85C \"\uAC00\uAE4C\uC6B4\uC9C0\" \uC5EC\uBD80\uAC00 \uC8FC\uC5B4\uC9C4 \uC9D1\uD569\uC774\uB2E4. \uADE0\uB4F1 \uACF5\uAC04 \uC704\uC5D0\uB294 \uADE0\uB4F1 \uC5F0\uC18D \uD568\uC218 \u00B7 \uCF54\uC2DC \uADF8\uBB3C \u00B7 \uC644\uBE44\uD654 \uB4F1\uC758 \uAC1C\uB150\uC744 \uC815\uC758\uD560 \uC218 \uC788\uB2E4. \uADE0\uB4F1 \uACF5\uAC04\uC758 \uAC1C\uB150\uC740 \uC704\uC0C1 \uACF5\uAC04\uACFC \uAC70\uB9AC \uACF5\uAC04\uC758 \uAC00\uC6B4\uB370\uC5D0 \uC788\uB2E4. \uC989, \uC784\uC758\uC758 \uAC70\uB9AC \uACF5\uAC04 \uC704\uC5D0\uB294 \uD45C\uC900\uC801\uC778 \uADE0\uB4F1 \uACF5\uAC04 \uAD6C\uC870\uAC00 \uC8FC\uC5B4\uC9C0\uBA70, \uC784\uC758\uC758 \uADE0\uB4F1 \uACF5\uAC04 \uC704\uC5D0\uB294 \uD45C\uC900\uC801\uC778 \uC704\uC0C1\uC774 \uC8FC\uC5B4\uC9C4\uB2E4. \uAC70\uB9AC \uACF5\uAC04\uC774 \uC544\uB2CC \uADE0\uB4F1 \uACF5\uAC04\uC758 \uB300\uD45C\uC801\uC778 \uC608\uB85C\uB294 \uC704\uC0C1\uAD70\uACFC \uCF64\uD329\uD2B8 \uD558\uC6B0\uC2A4\uB3C4\uB974\uD504 \uACF5\uAC04\uC774 \uC788\uB2E4."@ko . . "En topolog\u00EDa y an\u00E1lisis funcional, un espacio uniforme es un conjunto dotado de una estructura uniforme que permite estudiar conceptos como continuidad uniforme, completitud y convergencia uniforme. La diferencia esencial entre un espacio topol\u00F3gico y un espacio uniforme est\u00E1 en que en un espacio uniforme, se puede formalizar la idea de \"x1 est\u00E1 tan lejos de x2 como y1 lo est\u00E1 de y 2\" mientras que en un espacio topol\u00F3gico se puede formalizar solamente que \"un punto x est\u00E1 arbitrariamente cerca de un conjunto A\" (es decir, en el cierre de A) o, tal vez, que \"un entorno A de x es m\u00E1s peque\u00F1o que otro entorno B\", pero la estructura topol\u00F3gica sola no da idea de la proximidad relativa entre los puntos. Los espacios uniformes generalizan los espacios m\u00E9tricos y abarcan las topolog\u00EDas de los grupos topol\u00F3gicos y por lo tanto son la base de la mayor parte del an\u00E1lisis. Se deben a Henri Cartan y fueron introducidos a trav\u00E9s de Bourbaki."@es . "\uC77C\uBC18\uC704\uC0C1\uC218\uD559\uC5D0\uC11C \uADE0\uB4F1 \uACF5\uAC04(\u5747\u7B49\u7A7A\u9593, \uC601\uC5B4: uniform space)\uC740 \uB450 \uC810\uC774 \uC11C\uB85C \"\uAC00\uAE4C\uC6B4\uC9C0\" \uC5EC\uBD80\uAC00 \uC8FC\uC5B4\uC9C4 \uC9D1\uD569\uC774\uB2E4. \uADE0\uB4F1 \uACF5\uAC04 \uC704\uC5D0\uB294 \uADE0\uB4F1 \uC5F0\uC18D \uD568\uC218 \u00B7 \uCF54\uC2DC \uADF8\uBB3C \u00B7 \uC644\uBE44\uD654 \uB4F1\uC758 \uAC1C\uB150\uC744 \uC815\uC758\uD560 \uC218 \uC788\uB2E4. \uADE0\uB4F1 \uACF5\uAC04\uC758 \uAC1C\uB150\uC740 \uC704\uC0C1 \uACF5\uAC04\uACFC \uAC70\uB9AC \uACF5\uAC04\uC758 \uAC00\uC6B4\uB370\uC5D0 \uC788\uB2E4. \uC989, \uC784\uC758\uC758 \uAC70\uB9AC \uACF5\uAC04 \uC704\uC5D0\uB294 \uD45C\uC900\uC801\uC778 \uADE0\uB4F1 \uACF5\uAC04 \uAD6C\uC870\uAC00 \uC8FC\uC5B4\uC9C0\uBA70, \uC784\uC758\uC758 \uADE0\uB4F1 \uACF5\uAC04 \uC704\uC5D0\uB294 \uD45C\uC900\uC801\uC778 \uC704\uC0C1\uC774 \uC8FC\uC5B4\uC9C4\uB2E4. \uAC70\uB9AC \uACF5\uAC04\uC774 \uC544\uB2CC \uADE0\uB4F1 \uACF5\uAC04\uC758 \uB300\uD45C\uC801\uC778 \uC608\uB85C\uB294 \uC704\uC0C1\uAD70\uACFC \uCF64\uD329\uD2B8 \uD558\uC6B0\uC2A4\uB3C4\uB974\uD504 \uACF5\uAC04\uC774 \uC788\uB2E4."@ko . "En math\u00E9matiques, la notion d'espace uniforme, introduite en 1937 par Andr\u00E9 Weil, est une g\u00E9n\u00E9ralisation de celle d'espace m\u00E9trique. Une structure uniforme est une structure qui permet de d\u00E9finir la continuit\u00E9 uniforme. On peut y parvenir de deux mani\u00E8res diff\u00E9rentes, l'une en g\u00E9n\u00E9ralisant la notion de distance, l'autre avec une axiomatique proche de celle des espaces topologiques. On montre que ces deux approches sont \u00E9quivalentes."@fr . "Uniforme ruimte"@nl . . . . . "\u4E00\u69D8\u7A7A\u9593"@ja . . . . . . . . . . "Spazio uniforme"@it . "\u0420\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440"@uk . . . "\u5728\u62D3\u6251\u5B66\u9019\u500B\u6578\u5B78\u9818\u57DF\u88E1\uFF0C\u4E00\u81F4\u7A7A\u95F4\uFF08uniform space\uFF09\u662F\u6307\u5E26\u6709\u4E00\u81F4\u7ED3\u6784\u7684\u96C6\u5408\u3002\u4E00\u81F4\u7A7A\u95F4\u662F\u4E00\u500B\u62D3\u64B2\u7A7A\u9593\uFF0C\u6709\u53EF\u4EE5\u7528\u6765\u5B9A\u4E49\u5982\u5B8C\u5907\u6027\u3001\u4E00\u81F4\u8FDE\u7EED\u53CA\u4E00\u81F4\u6536\u655B\u7B49\u4E00\u81F4\u6027\u8CEA\u7684\u9644\u52A0\u7ED3\u6784\u3002 \u4E00\u81F4\u7ED3\u6784\u548C\u62D3\u6251\u7ED3\u6784\u4E4B\u95F4\u7684\u6982\u5FF5\u533A\u522B\u5728\u65BC\uFF0C\u4E00\u81F4\u7A7A\u95F4\u53EF\u4EE5\u5F62\u5F0F\u5316\u6709\u5173\u4E8E\u76F8\u5BF9\u90BB\u8FD1\u6027\u53CA\u70B9\u95F4\u4E34\u8FD1\u6027\u7B49\u7279\u5B9A\u6982\u5FF5\u3002\u6362\u53E5\u8BDD\u8BF4\uFF0C\u300Cx \u90BB\u8FD1\u4E8Ea \u80DC\u8FC7y \u90BB\u8FD1\u4E8Eb\u300D\u4E4B\u985E\u7684\u6982\u5FF5\uFF0C\u5728\u4E00\u81F4\u7A7A\u95F4\u4E2D\u662F\u6709\u610F\u4E49\u7684\u3002\u800C\u76F8\u5BF9\u7684\uFF0C\u5728\u4E00\u822C\u62D3\u6251\u7A7A\u95F4\u5185\uFF0C\u7ED9\u5B9A\u96C6\u5408A \u548CB\uFF0C\u6709\u610F\u4E49\u7684\u6982\u5FF5\u53EA\u6709\uFF1A\u70B9x \u80FD\u201C\u4EFB\u610F\u90BB\u8FD1\u201DA\uFF08\u4EA6\u5373\u5728A \u7684\u95ED\u5305\u5167\uFF09\uFF1B\u6216\u662F\u548CB\u76F8\u6BD4\uFF0CA \u662Fx \u7684\u201C\u8F03\u5C0F\u90BB\u57DF\u201D\uFF0C\u4F46\u70B9\u95F4\u90BB\u8FD1\u6027\u548C\u76F8\u5BF9\u90BB\u8FD1\u6027\u5C31\u4E0D\u80FD\u53EA\u7528\u62D3\u6251\u7ED3\u6784\u4F86\u63CF\u8FF0\u4E86\u3002 \u4E00\u81F4\u7A7A\u95F4\u5E7F\u7FA9\u5316\u4E86\u5EA6\u91CF\u7A7A\u95F4\u548C\u62D3\u6251\u7FA4\uFF0C\u56E0\u6B64\u6210\u70BA\u591A\u6570\u6570\u5B66\u5206\u6790\u7684\u6839\u57FA\u3002"@zh . "26253"^^ . . . "En topolog\u00EDa y an\u00E1lisis funcional, un espacio uniforme es un conjunto dotado de una estructura uniforme que permite estudiar conceptos como continuidad uniforme, completitud y convergencia uniforme. La diferencia esencial entre un espacio topol\u00F3gico y un espacio uniforme est\u00E1 en que en un espacio uniforme, se puede formalizar la idea de \"x1 est\u00E1 tan lejos de x2 como y1 lo est\u00E1 de y 2\" mientras que en un espacio topol\u00F3gico se puede formalizar solamente que \"un punto x est\u00E1 arbitrariamente cerca de un conjunto A\" (es decir, en el cierre de A) o, tal vez, que \"un entorno A de x es m\u00E1s peque\u00F1o que otro entorno B\", pero la estructura topol\u00F3gica sola no da idea de la proximidad relativa entre los puntos."@es . . . . "In de topologie, een deelgebied van de wiskunde, is een uniforme ruimte een verzameling voorzien van een uniforme structuur (uniformiteit). Uniforme ruimten veralgemenen bepaalde eigenschappen en begrippen van metrische ruimten die weliswaar geen topologische invarianten zijn, maar die nauw verwant zijn met topologische eigenschappen, bijvoorbeeld Cauchyrijen en volledigheid, uniforme continu\u00EFteit en uniforme convergentie."@nl . "\u0423 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0456\u0439 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0457 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u043E\u0457 \u0441\u0442\u0440\u0443\u043A\u0442\u0443\u0440\u0438 \u0456 \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0442\u044C \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0438\u0442\u0438 \u0442\u0430\u043A\u0456 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0430\u043D\u0430\u043B\u0456\u0437\u0443 \u0456, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456\u0432, \u044F\u043A \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u0430 \u0437\u0431\u0456\u0436\u043D\u0456\u0441\u0442\u044C, \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u0430 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0456\u0441\u0442\u044C, \u043F\u043E\u0432\u043D\u043E\u0442\u0430 \u043D\u0430 \u0431\u0456\u043B\u044C\u0448 \u0448\u0438\u0440\u043E\u043A\u0438\u0439 \u043A\u043B\u0430\u0441 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456\u0432. \u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0432\u043F\u0435\u0440\u0448\u0435 \u0431\u0443\u043B\u043E \u0432\u0432\u0435\u0434\u0435\u043D\u0435 \u0443 1937 \u0440\u043E\u0446\u0456 \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u0438\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u043C \u0410\u043D\u0434\u0440\u0435 \u0412\u0435\u0439\u043B\u0435\u043C."@uk . "\u0423 \u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0456\u0439 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0457 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u043E\u0457 \u0441\u0442\u0440\u0443\u043A\u0442\u0443\u0440\u0438 \u0456 \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0443 \u0434\u043E\u0437\u0432\u043E\u043B\u044F\u044E\u0442\u044C \u0443\u0437\u0430\u0433\u0430\u043B\u044C\u043D\u0438\u0442\u0438 \u0442\u0430\u043A\u0456 \u043F\u043E\u043D\u044F\u0442\u0442\u044F \u0430\u043D\u0430\u043B\u0456\u0437\u0443 \u0456, \u0437\u043E\u043A\u0440\u0435\u043C\u0430 \u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456\u0432, \u044F\u043A \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u0430 \u0437\u0431\u0456\u0436\u043D\u0456\u0441\u0442\u044C, \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u0430 \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0456\u0441\u0442\u044C, \u043F\u043E\u0432\u043D\u043E\u0442\u0430 \u043D\u0430 \u0431\u0456\u043B\u044C\u0448 \u0448\u0438\u0440\u043E\u043A\u0438\u0439 \u043A\u043B\u0430\u0441 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456\u0432. \u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0432\u043F\u0435\u0440\u0448\u0435 \u0431\u0443\u043B\u043E \u0432\u0432\u0435\u0434\u0435\u043D\u0435 \u0443 1937 \u0440\u043E\u0446\u0456 \u0444\u0440\u0430\u043D\u0446\u0443\u0437\u044C\u043A\u0438\u043C \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u043E\u043C \u0410\u043D\u0434\u0440\u0435 \u0412\u0435\u0439\u043B\u0435\u043C."@uk . . . . . . . . . . "In topologia, uno spazio uniforme \u00E8 uno spazio topologico dotato di una struttura uniforme, che consente di definire propriet\u00E0 uniformi, come la completezza, la continuit\u00E0 uniforme e la convergenza uniforme. Negli spazi uniformi \u00E8 possibile definire alcune nozioni di vicinanza relativa e vicinanza tra punti, che non \u00E8 possibile stabilire con il solo utilizzo della struttura topologica. Ad esempio, dati i punti , , , , \u00E8 possibile stabilire che \u00E8 pi\u00F9 vicino ad di quanto sia vicino a . Gli spazi uniformi possono essere visti come una generalizzazione degli spazi metrici e dei gruppi topologici, e permettono la definizione di gran parte dei concetti dell'analisi matematica. La struttura uniforme, e gli altri concetti ad essa collegati, fu definita esplicitamente da Andr\u00E9 Weil nel 1937, mediante l'utilizzo di pseudometriche. Successivamente Nicolas Bourbaki forn\u00EC la definizione in termini di entourage e John Tukey la diede in termini di ricoprimenti uniformi. Queste definizioni sono descritte nei paragrafi sottostanti."@it . . . "\u4E00\u69D8\u7A7A\u9593\uFF08\u3044\u3061\u3088\u3046\u304F\u3046\u304B\u3093\u3001\u82F1: uniform space\uFF09\u3068\u306F\u3001\u4E00\u69D8\u69CB\u9020\u3068\u3044\u3046\u69CB\u9020\u3092\u5099\u3048\u305F\u96C6\u5408\u3067\u3042\u308B\u3002\u4E00\u69D8\u69CB\u9020\u306F\u64EC\u8DDD\u96E2\u69CB\u9020\u3068\u4F4D\u76F8\u69CB\u9020\u306E\u4E2D\u9593\u306E\u5F37\u3055\u3092\u6301\u3061\u3001\u4F4D\u76F8\u69CB\u9020\u3060\u3051\u3067\u306F\u5B9A\u7FA9\u3067\u304D\u306A\u3044\u4E00\u69D8\u9023\u7D9A\u6027\u3001\u30B3\u30FC\u30B7\u30FC\u5217\u3001\u5B8C\u5099\u6027\u3001\u4E00\u69D8\u9023\u7D9A\u6027\u3001\u4E00\u69D8\u6709\u754C\u6027\u3001\u5168\u6709\u754C\u6027\u306A\u3069\u304C\u5B9A\u7FA9\u3067\u304D\u308B\u3002 \u307E\u305F\u64EC\u8DDD\u96E2\u7A7A\u9593\u306E\u307F\u306A\u3089\u305A\u4F4D\u76F8\u7FA4\uFF08\u3068\u304F\u306B\u4F4D\u76F8\u30D9\u30AF\u30C8\u30EB\u7A7A\u9593\uFF09\u306B\u95A2\u3057\u3066\u3082\u81EA\u7136\u306A\u4E00\u69D8\u69CB\u9020\u304C\u5B9A\u307E\u308B\u4E8B\u304C\u77E5\u3089\u308C\u3066\u3044\u308B\u70BA\u3001\u4E00\u69D8\u7A7A\u9593\u306E\u6982\u5FF5\u306F\u95A2\u6570\u89E3\u6790\u5B66\u306B\u304A\u3044\u3066\u6709\u76CA\u3067\u3042\u308B\u3002 \u4F4D\u76F8\u7A7A\u9593\u3068\u306E\u9055\u3044\u306F\u3001\u4F4D\u76F8\u7A7A\u9593\u304C\u53CE\u675F\u6027\u3001\u3059\u306A\u308F\u3061\u70B9\u306B\u300C\u8FD1\u3065\u304F\u300D\u4E8B\u3092\u5B9A\u7FA9\u53EF\u80FD\u306A\u6982\u5FF5\u3067\u3042\u308B\u306E\u306B\u5BFE\u3057\u3001\u4E00\u69D8\u7A7A\u9593\u3067\u306F\u3042\u308B\u70B9\u304C\u5225\u306E\u70B9\u306B\u300C\u8FD1\u3044\u300D\u4E8B\u304C\u5B9A\u7FA9\u3067\u304D\u308B\u3002\u3057\u304B\u3057\u3053\u306E\u300C\u8FD1\u3055\u300D\u306F\u64EC\u8DDD\u96E2\u69CB\u9020\u306E\u3088\u3046\u306B\u5B9F\u6570\u5024\u3067\u5168\u9806\u5E8F\u3065\u3051\u3055\u308C\u3066\u304A\u3089\u305A\u3001\u8FD1\u7E01\u3068\u547C\u3070\u308C\u308B\u90E8\u5206\u96C6\u5408\u306B\u5C5E\u3059\u308B\u304B\u3069\u3046\u304B\u3067\u5224\u65AD\u3059\u308B\u534A\u9806\u5E8F\u7684\u306A\u3082\u306E\u3067\u3042\u308B\u3002"@ja . . . . . . . . "Uniform space"@en . . . . . . . . . . . . . . . . "\uADE0\uB4F1 \uACF5\uAC04"@ko . . "1123426020"^^ . . . . . . . . . . "In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure that is used to define uniform properties such as completeness, uniform continuity and uniform convergence. Uniform spaces generalize metric spaces and topological groups, but the concept is designed to formulate the weakest axioms needed for most proofs in analysis. In addition to the usual properties of a topological structure, in a uniform space one formalizes the notions of relative closeness and closeness of points. In other words, ideas like \"x is closer to a than y is to b\" make sense in uniform spaces. By comparison, in a general topological space, given sets A,B it is meaningful to say that a point x is arbitrarily close to A (i.e., in the closure of A), or perhaps that A is a smaller neighborhood of x than B, but notions of closeness of points and relative closeness are not described well by topological structure alone."@en .