. . "In functional analysis and related areas of mathematics, a barrelled space (also written barreled space) is a topological vector space (TVS) for which every barrelled set in the space is a neighbourhood for the zero vector. A barrelled set or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied because a form of the Banach\u2013Steinhaus theorem still holds for them. Barrelled spaces were introduced by Bourbaki."@en . . . . . . "If is a barrelled TVS over the complex numbers and is a subset of the continuous dual space of , then the following are equivalent:\n\n is weakly bounded;\n is strongly bounded;\n is equicontinuous;\n is relatively compact in the weak dual topology."@en . "\u0411\u043E\u0447\u0435\u0447\u043D\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E"@ru . . "\u0411\u043E\u0447\u043A\u043E\u044E \u0432 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u043E\u043C\u0443 \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u043C\u0443 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043F\u0456\u0434\u043C\u043D\u043E\u0436\u0438\u043D\u0430, \u044F\u043A\u0430 \u0440\u0430\u0434\u0456\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0430, \u0437\u0430\u043A\u0440\u0443\u0433\u043B\u0435\u043D\u0430 \u0456 \u0437\u0430\u043C\u043A\u043D\u0443\u0442\u0430. \u041B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0431\u043E\u0447\u043A\u043E\u0432\u0438\u043C, \u044F\u043A\u0449\u043E \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u0431\u043E\u0447\u043A\u0430 \u0432 \u043D\u044C\u043E\u043C\u0443 \u0454 \u043E\u043A\u043E\u043B\u043E\u043C \u043D\u0443\u043B\u044F \u0430\u0431\u043E, \u0449\u043E \u0442\u0435 \u0436 \u0441\u0430\u043C\u0435, \u0431\u043E\u0447\u043A\u043E\u0432\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u2014 \u0446\u0435 \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440, \u0432 \u044F\u043A\u043E\u043C\u0443 \u0441\u0456\u043C\u0435\u0439\u0441\u0442\u0432\u043E \u0432\u0441\u0456\u0445 \u0431\u043E\u0447\u043E\u043A \u0443\u0442\u0432\u043E\u0440\u044E\u0454 \u0431\u0430\u0437\u0438\u0441 (\u0430\u0431\u043E \u043D\u0430 \u044F\u043A\u043E\u043C\u0443 \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u043F\u0435\u0440\u0435\u0434\u043D\u043E\u0440\u043C\u0430 \u043D\u0430\u043F\u0456\u0432\u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0430 \u0437\u043D\u0438\u0437\u0443, \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0430). \u0411\u0443\u0434\u044C-\u044F\u043A\u0438\u0439 \u0431\u0435\u0440\u0456\u0432\u0441\u044C\u043A\u0438\u0439 \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u0431\u043E\u0447\u043A\u043E\u0432\u0438\u0439. \u0417\u043E\u043A\u0440\u0435\u043C\u0430, \u0432\u0441\u0456 \u0431\u0430\u043D\u0430\u0445\u043E\u0432\u0456 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0438 \u0456 \u0432\u0441\u0456 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0438 \u0424\u0440\u0435\u0448\u0435 \u0431\u043E\u0447\u043A\u043E\u0432\u0456."@uk . . . . . "In matematica, in particolare in analisi funzionale, uno spazio botte (in inglese barrelled space) \u00E8 uno spazio vettoriale topologico localmente convesso che condivide diverse caratteristiche degli spazi di Fr\u00E9chet. Gli spazi botte, introdotti dal gruppo di matematici Nicolas Bourbaki, sono studiati soprattutto perch\u00E9 per essi \u00E8 valida una forma del principio dell'uniforme limitatezza. Un insieme \u00E8 detto bilanciato se: L'insieme bilanciato \u00E8 detto assorbente se esiste tale che: Un insieme botte \u00E8 un insieme convesso, bilanciato, assorbente e chiuso. Uno spazio botte \u00E8 uno spazio vettoriale topologico con una topologia localmente convessa tale per cui ogni insieme botte \u00E8 un intorno del vettore nullo."@it . . "Tonnelierte R\u00E4ume sind spezielle lokalkonvexe Vektorr\u00E4ume, in denen der Satz von Banach-Steinhaus gilt. Diese R\u00E4ume lassen sich durch ihre Nullumgebungsbasen charakterisieren."@de . . . . "1112416982"^^ . . . . . . . . . . . . . . . . "\u51FD\u6570\u89E3\u6790\u5B66\u304A\u3088\u3073\u95A2\u9023\u3059\u308B\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u6A3D\u578B\u7A7A\u9593\uFF08\u305F\u308B\u304C\u305F\u304F\u3046\u304B\u3093\u3001\u82F1: barrelled space\uFF09\u3068\u306F\u3001\u305D\u306E\u7A7A\u9593\u306E\u3059\u3079\u3066\u306E\u6A3D\u578B\u96C6\u5408\u304C\u96F6\u30D9\u30AF\u30C8\u30EB\u306E\u8FD1\u508D\u3067\u3042\u308B\u3088\u3046\u306A\u30CF\u30A6\u30B9\u30C9\u30EB\u30D5\u4F4D\u76F8\u7DDA\u578B\u7A7A\u9593\u306E\u3053\u3068\u3092\u3044\u3046\u3002\u3053\u3053\u3067\u3001\u3042\u308B\u4F4D\u76F8\u7DDA\u578B\u7A7A\u9593\u306B\u304A\u3051\u308B\u6A3D\u578B\u96C6\u5408 (barrel) \u3068\u306F\u3001\u51F8\u3001\u5747\u8861\u3001\u4F75\u5451\u304B\u3064\u9589\u3067\u3042\u308B\u96C6\u5408\u306E\u3053\u3068\u3092\u3044\u3046\u3002\u6A3D\u578B\u7A7A\u9593\u304C\u7814\u7A76\u3055\u308C\u308B\u7406\u7531\u3068\u3057\u3066\u3001\u306E\u4E00\u7A2E\u304C\u305D\u308C\u3089\u306B\u5BFE\u3057\u3066\u6210\u7ACB\u3059\u308B\u3053\u3068\u304C\u6319\u3052\u3089\u308C\u308B\u3002"@ja . "Tonnelierter Raum"@de . "\u51FD\u6570\u89E3\u6790\u5B66\u304A\u3088\u3073\u95A2\u9023\u3059\u308B\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u6A3D\u578B\u7A7A\u9593\uFF08\u305F\u308B\u304C\u305F\u304F\u3046\u304B\u3093\u3001\u82F1: barrelled space\uFF09\u3068\u306F\u3001\u305D\u306E\u7A7A\u9593\u306E\u3059\u3079\u3066\u306E\u6A3D\u578B\u96C6\u5408\u304C\u96F6\u30D9\u30AF\u30C8\u30EB\u306E\u8FD1\u508D\u3067\u3042\u308B\u3088\u3046\u306A\u30CF\u30A6\u30B9\u30C9\u30EB\u30D5\u4F4D\u76F8\u7DDA\u578B\u7A7A\u9593\u306E\u3053\u3068\u3092\u3044\u3046\u3002\u3053\u3053\u3067\u3001\u3042\u308B\u4F4D\u76F8\u7DDA\u578B\u7A7A\u9593\u306B\u304A\u3051\u308B\u6A3D\u578B\u96C6\u5408 (barrel) \u3068\u306F\u3001\u51F8\u3001\u5747\u8861\u3001\u4F75\u5451\u304B\u3064\u9589\u3067\u3042\u308B\u96C6\u5408\u306E\u3053\u3068\u3092\u3044\u3046\u3002\u6A3D\u578B\u7A7A\u9593\u304C\u7814\u7A76\u3055\u308C\u308B\u7406\u7531\u3068\u3057\u3066\u3001\u306E\u4E00\u7A2E\u304C\u305D\u308C\u3089\u306B\u5BFE\u3057\u3066\u6210\u7ACB\u3059\u308B\u3053\u3068\u304C\u6319\u3052\u3089\u308C\u308B\u3002"@ja . . . . . . . . . . "In de wiskunde, meer bepaald in de functionaalanalyse, wordt het begrip tonruimte gehanteerdals veralgemening van Fr\u00E9chet-ruimten (en dus in het bijzonder van Banachruimten). Het ontleent zijnbelang aan het feit dat de definitie invariant is onder de vorming van finale topologie\u00EBn."@nl . . . . "En analyse fonctionnelle et dans les domaines proches des math\u00E9matiques, les espaces tonnel\u00E9s sont des espaces vectoriels topologiques o\u00F9 tout ensemble tonnel\u00E9 - ou tonneau - de l'espace est un voisinage du vecteur nul. La raison principale de leur importance est qu'ils sont exactement ceux pour lesquels le th\u00E9or\u00E8me de Banach-Steinhaus s'applique."@fr . "\u0411\u043E\u0447\u043A\u043E\u0439 \u0432 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u043E\u043C \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043F\u043E\u0434\u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E, \u043A\u043E\u0442\u043E\u0440\u043E\u0435 , \u0437\u0430\u043A\u0440\u0443\u0433\u043B\u0435\u043D\u043E \u0438 \u0437\u0430\u043C\u043A\u043D\u0443\u0442\u043E. \u041B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u0432\u044B\u043F\u0443\u043A\u043B\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0431\u043E\u0447\u0435\u0447\u043D\u044B\u043C, \u0435\u0441\u043B\u0438 \u0432\u0441\u044F\u043A\u0430\u044F \u0431\u043E\u0447\u043A\u0430 \u0432 \u043D\u0451\u043C \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043E\u043A\u0440\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u044C\u044E \u043D\u0443\u043B\u044F \u0438\u043B\u0438, \u0447\u0442\u043E \u0442\u043E \u0436\u0435 \u0441\u0430\u043C\u043E\u0435, \u0431\u043E\u0447\u0435\u0447\u043D\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u2014 \u044D\u0442\u043E \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u0432\u044B\u043F\u0443\u043A\u043B\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0441\u0435\u043C\u0435\u0439\u0441\u0442\u0432\u043E \u0432\u0441\u0435\u0445 \u0431\u043E\u0447\u0435\u043A \u043E\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0431\u0430\u0437\u0438\u0441 (\u0438\u043B\u0438 \u043D\u0430 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0432\u0441\u044F\u043A\u0430\u044F \u043F\u0440\u0435\u0434\u043D\u043E\u0440\u043C\u0430 \u043F\u043E\u043B\u0443\u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u0430\u044F \u0441\u043D\u0438\u0437\u0443, \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u0430). \u0412\u0441\u044F\u043A\u043E\u0435 \u0431\u044D\u0440\u043E\u0432\u0441\u043A\u043E\u0435 \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u0432\u044B\u043F\u0443\u043A\u043B\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u0431\u043E\u0447\u0435\u0447\u043D\u043E. \u0412 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0432\u0441\u0435 \u0431\u0430\u043D\u0430\u0445\u043E\u0432\u044B \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 \u0438 \u0432\u0441\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 \u0424\u0440\u0435\u0448\u0435 \u0431\u043E\u0447\u0435\u0447\u043D\u044B."@ru . . . . . . . . . "Closed Graph Theorem"@en . . . "Let be a barrelled TVS and be a locally convex TVS. \nLet be a subset of the space of continuous linear maps from into . \nThe following are equivalent:\n\n is bounded for the topology of pointwise convergence;\n is bounded for the topology of bounded convergence;\n is equicontinuous."@en . . "\uD568\uC218\uD574\uC11D\uD559\uC5D0\uC11C \uBC30\uB7F4 \uACF5\uAC04(\uC601\uC5B4: barreled space, \uD504\uB791\uC2A4\uC5B4: espace tonnel\u00E9)\uC740 \uACF5\uAC04\uC758 \uBAA8\uB4E0 \uBC30\uB7F4 \uC9D1\uD569\uC774 \uC601\uBCA1\uD130\uC758 \uADFC\uBC29\uC778 \uD558\uC6B0\uC2A4\uB3C4\uB974\uD504 \uC704\uC0C1 \uBCA1\uD130 \uACF5\uAC04\uC774\uB2E4. \uC704\uC0C1 \uBCA1\uD130 \uACF5\uAC04\uC5D0\uC11C \uBC30\uB7F4 \uC9D1\uD569 \uB610\uB294 \uBC30\uB7F4\uC740 \uBCFC\uB85D, \uADE0\uD615, \uD761\uC218 \uADF8\uB9AC\uACE0 \uB2EB\uD78C \uC9D1\uD569\uC774\uB2E4. \uBC30\uB7F4 \uACF5\uAC04\uC740 \uBC14\uB098\uD750-\uC2A4\uD14C\uC778\uD558\uC6B0\uC2A4 \uC815\uB9AC\uC758 \uD55C \uD615\uD0DC\uAC00 \uC774 \uACF5\uAC04\uC5D0 \uC801\uC6A9\uB418\uAE30 \uB54C\uBB38\uC5D0 \uC5F0\uAD6C\uB418\uC5C8\uB2E4."@ko . . . . . . "Spazio botte"@it . "Tonnelierte R\u00E4ume sind spezielle lokalkonvexe Vektorr\u00E4ume, in denen der Satz von Banach-Steinhaus gilt. Diese R\u00E4ume lassen sich durch ihre Nullumgebungsbasen charakterisieren."@de . . . . . . . . . . . . . . . . . . "Espace tonnel\u00E9"@fr . . "En analyse fonctionnelle et dans les domaines proches des math\u00E9matiques, les espaces tonnel\u00E9s sont des espaces vectoriels topologiques o\u00F9 tout ensemble tonnel\u00E9 - ou tonneau - de l'espace est un voisinage du vecteur nul. La raison principale de leur importance est qu'ils sont exactement ceux pour lesquels le th\u00E9or\u00E8me de Banach-Steinhaus s'applique."@fr . "In matematica, in particolare in analisi funzionale, uno spazio botte (in inglese barrelled space) \u00E8 uno spazio vettoriale topologico localmente convesso che condivide diverse caratteristiche degli spazi di Fr\u00E9chet. Gli spazi botte, introdotti dal gruppo di matematici Nicolas Bourbaki, sono studiati soprattutto perch\u00E9 per essi \u00E8 valida una forma del principio dell'uniforme limitatezza. Un insieme \u00E8 detto bilanciato se: L'insieme bilanciato \u00E8 detto assorbente se esiste tale che: Un insieme botte \u00E8 un insieme convesso, bilanciato, assorbente e chiuso."@it . "\uBC30\uB7F4 \uACF5\uAC04"@ko . "23576"^^ . "\uD568\uC218\uD574\uC11D\uD559\uC5D0\uC11C \uBC30\uB7F4 \uACF5\uAC04(\uC601\uC5B4: barreled space, \uD504\uB791\uC2A4\uC5B4: espace tonnel\u00E9)\uC740 \uACF5\uAC04\uC758 \uBAA8\uB4E0 \uBC30\uB7F4 \uC9D1\uD569\uC774 \uC601\uBCA1\uD130\uC758 \uADFC\uBC29\uC778 \uD558\uC6B0\uC2A4\uB3C4\uB974\uD504 \uC704\uC0C1 \uBCA1\uD130 \uACF5\uAC04\uC774\uB2E4. \uC704\uC0C1 \uBCA1\uD130 \uACF5\uAC04\uC5D0\uC11C \uBC30\uB7F4 \uC9D1\uD569 \uB610\uB294 \uBC30\uB7F4\uC740 \uBCFC\uB85D, \uADE0\uD615, \uD761\uC218 \uADF8\uB9AC\uACE0 \uB2EB\uD78C \uC9D1\uD569\uC774\uB2E4. \uBC30\uB7F4 \uACF5\uAC04\uC740 \uBC14\uB098\uD750-\uC2A4\uD14C\uC778\uD558\uC6B0\uC2A4 \uC815\uB9AC\uC758 \uD55C \uD615\uD0DC\uAC00 \uC774 \uACF5\uAC04\uC5D0 \uC801\uC6A9\uB418\uAE30 \uB54C\uBB38\uC5D0 \uC5F0\uAD6C\uB418\uC5C8\uB2E4."@ko . . . "In functional analysis and related areas of mathematics, a barrelled space (also written barreled space) is a topological vector space (TVS) for which every barrelled set in the space is a neighbourhood for the zero vector. A barrelled set or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied because a form of the Banach\u2013Steinhaus theorem still holds for them. Barrelled spaces were introduced by Bourbaki."@en . "\u0411\u043E\u0447\u043A\u043E\u044E \u0432 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0456\u0447\u043D\u043E\u043C\u0443 \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u043C\u0443 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0456 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043F\u0456\u0434\u043C\u043D\u043E\u0436\u0438\u043D\u0430, \u044F\u043A\u0430 \u0440\u0430\u0434\u0456\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0430, \u0437\u0430\u043A\u0440\u0443\u0433\u043B\u0435\u043D\u0430 \u0456 \u0437\u0430\u043C\u043A\u043D\u0443\u0442\u0430. \u041B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u0431\u043E\u0447\u043A\u043E\u0432\u0438\u043C, \u044F\u043A\u0449\u043E \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u0431\u043E\u0447\u043A\u0430 \u0432 \u043D\u044C\u043E\u043C\u0443 \u0454 \u043E\u043A\u043E\u043B\u043E\u043C \u043D\u0443\u043B\u044F \u0430\u0431\u043E, \u0449\u043E \u0442\u0435 \u0436 \u0441\u0430\u043C\u0435, \u0431\u043E\u0447\u043A\u043E\u0432\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u2014 \u0446\u0435 \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440, \u0432 \u044F\u043A\u043E\u043C\u0443 \u0441\u0456\u043C\u0435\u0439\u0441\u0442\u0432\u043E \u0432\u0441\u0456\u0445 \u0431\u043E\u0447\u043E\u043A \u0443\u0442\u0432\u043E\u0440\u044E\u0454 \u0431\u0430\u0437\u0438\u0441 (\u0430\u0431\u043E \u043D\u0430 \u044F\u043A\u043E\u043C\u0443 \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u043F\u0435\u0440\u0435\u0434\u043D\u043E\u0440\u043C\u0430 \u043D\u0430\u043F\u0456\u0432\u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0430 \u0437\u043D\u0438\u0437\u0443, \u043D\u0435\u043F\u0435\u0440\u0435\u0440\u0432\u043D\u0430). \u0411\u0443\u0434\u044C-\u044F\u043A\u0438\u0439 \u0431\u0435\u0440\u0456\u0432\u0441\u044C\u043A\u0438\u0439 \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u043E\u043F\u0443\u043A\u043B\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440 \u0431\u043E\u0447\u043A\u043E\u0432\u0438\u0439. \u0417\u043E\u043A\u0440\u0435\u043C\u0430, \u0432\u0441\u0456 \u0431\u0430\u043D\u0430\u0445\u043E\u0432\u0456 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0438 \u0456 \u0432\u0441\u0456 \u043F\u0440\u043E\u0441\u0442\u043E\u0440\u0438 \u0424\u0440\u0435\u0448\u0435 \u0431\u043E\u0447\u043A\u043E\u0432\u0456."@uk . . "Every closed linear operator from a Hausdorff barrelled TVS into a complete metrizable TVS is continuous."@en . . "In de wiskunde, meer bepaald in de functionaalanalyse, wordt het begrip tonruimte gehanteerdals veralgemening van Fr\u00E9chet-ruimten (en dus in het bijzonder van Banachruimten). Het ontleent zijnbelang aan het feit dat de definitie invariant is onder de vorming van finale topologie\u00EBn."@nl . . . . . . . . . . . "\u6A3D\u578B\u7A7A\u9593"@ja . . . . . . . . . . . . . . . . "\u0411\u043E\u0447\u043A\u043E\u0439 \u0432 \u0442\u043E\u043F\u043E\u043B\u043E\u0433\u0438\u0447\u0435\u0441\u043A\u043E\u043C \u0432\u0435\u043A\u0442\u043E\u0440\u043D\u043E\u043C \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0435 \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043F\u043E\u0434\u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E, \u043A\u043E\u0442\u043E\u0440\u043E\u0435 , \u0437\u0430\u043A\u0440\u0443\u0433\u043B\u0435\u043D\u043E \u0438 \u0437\u0430\u043C\u043A\u043D\u0443\u0442\u043E. \u041B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u0432\u044B\u043F\u0443\u043A\u043B\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u0431\u043E\u0447\u0435\u0447\u043D\u044B\u043C, \u0435\u0441\u043B\u0438 \u0432\u0441\u044F\u043A\u0430\u044F \u0431\u043E\u0447\u043A\u0430 \u0432 \u043D\u0451\u043C \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u043E\u043A\u0440\u0435\u0441\u0442\u043D\u043E\u0441\u0442\u044C\u044E \u043D\u0443\u043B\u044F \u0438\u043B\u0438, \u0447\u0442\u043E \u0442\u043E \u0436\u0435 \u0441\u0430\u043C\u043E\u0435, \u0431\u043E\u0447\u0435\u0447\u043D\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u2014 \u044D\u0442\u043E \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u0432\u044B\u043F\u0443\u043A\u043B\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E, \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0441\u0435\u043C\u0435\u0439\u0441\u0442\u0432\u043E \u0432\u0441\u0435\u0445 \u0431\u043E\u0447\u0435\u043A \u043E\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u0431\u0430\u0437\u0438\u0441 (\u0438\u043B\u0438 \u043D\u0430 \u043A\u043E\u0442\u043E\u0440\u043E\u043C \u0432\u0441\u044F\u043A\u0430\u044F \u043F\u0440\u0435\u0434\u043D\u043E\u0440\u043C\u0430 \u043F\u043E\u043B\u0443\u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u0430\u044F \u0441\u043D\u0438\u0437\u0443, \u043D\u0435\u043F\u0440\u0435\u0440\u044B\u0432\u043D\u0430). \u0412\u0441\u044F\u043A\u043E\u0435 \u0431\u044D\u0440\u043E\u0432\u0441\u043A\u043E\u0435 \u043B\u043E\u043A\u0430\u043B\u044C\u043D\u043E \u0432\u044B\u043F\u0443\u043A\u043B\u043E\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u043E \u0431\u043E\u0447\u0435\u0447\u043D\u043E. \u0412 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u0432\u0441\u0435 \u0431\u0430\u043D\u0430\u0445\u043E\u0432\u044B \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 \u0438 \u0432\u0441\u0435 \u043F\u0440\u043E\u0441\u0442\u0440\u0430\u043D\u0441\u0442\u0432\u0430 \u0424\u0440\u0435\u0448\u0435 \u0431\u043E\u0447\u0435\u0447\u043D\u044B."@ru . . . . . . . . . . . . . "Tonruimte"@nl . . "1733592"^^ . . . "Theorem"@en . . . "Barrelled space"@en . . "\u0411\u043E\u0447\u043A\u043E\u0432\u0438\u0439 \u043F\u0440\u043E\u0441\u0442\u0456\u0440"@uk . .