. . . . . . . . . . "1789812"^^ . . . . . . . . . "Proof of part"@en . . . . . . "true"@en . . . "In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935."@en . . . . . . . . . . . . . . "( \uC77C\uBC18\uC801\uC778 \uC720\uACC4 \uC9D1\uD569\uC5D0 \uAD00\uD574\uC11C\uB294 \uC720\uACC4 \uC9D1\uD569 \uBB38\uC11C\uB97C \uBCF4\uC2ED\uC2DC\uC624.) \uD568\uC218\uD574\uC11D\uD559\uACFC \uC218\uD559\uC758 \uAD00\uB828 \uBD84\uC57C\uC5D0\uC11C, \uC601\uBCA1\uD130\uC758 \uBAA8\uB4E0 \uADFC\uBC29\uC744 \uD33D\uCC3D\uC2DC\uCF1C\uC11C \uC704\uC0C1 \uBCA1\uD130 \uACF5\uAC04\uC758 \uC5B4\uB5A4 \uC9D1\uD569\uC744 \uD3EC\uD568\uD560 \uC218 \uC788\uC73C\uBA74 \uC720\uACC4 \uC9D1\uD569 \uB610\uB294 \uD3F0 \uB178\uC774\uB9CC \uC720\uACC4 \uC9D1\uD569\uC774\uB77C\uACE0 \uBD88\uB9B0\uB2E4. \uBC18\uB300\uB85C \uC9D1\uD569\uC774 \uC720\uACC4\uAC00 \uC544\uB2C8\uBA74 \uBB34\uACC4 \uC9D1\uD569\uC774\uB77C\uACE0 \uBD88\uB9B0\uB2E4. \uC720\uACC4 \uC9D1\uD569\uC758 \uC740 \uC808\uB300 \uBCFC\uB85D \uC9D1\uD569\uC774\uACE0 \uD761\uC218 \uC9D1\uD569\uC774\uAE30 \uB54C\uBB38\uC5D0, \uC720\uACC4\uC9D1\uD569\uC740 \uC778 \uC758 \uC744 \uC815\uC758\uD558\uB294 \uC77C\uBC18\uC801\uC778 \uBC29\uBC95\uC774\uB2E4. \uC774 \uAC1C\uB150\uC740 1935\uB144\uC5D0 \uC874 \uD3F0 \uB178\uC774\uB9CC\uACFC \uC548\uB4DC\uB808\uC774 \uCF5C\uBAA8\uACE0\uB85C\uD504\uC5D0 \uC758\uD574\uC11C \uCC98\uC74C\uC73C\uB85C \uB098\uD0C0\uB098\uAC8C \uB418\uC5C8\uB2E4."@ko . . . . . . . . . . "24983"^^ . . . . . . . . . . . . "\uC720\uACC4 \uC9D1\uD569 (\uC704\uC0C1\uC801 \uBCA1\uD130 \uACF5\uAC04)"@ko . . . "Bounded set (topological vector space)"@en . . . . . "no"@en . . . . . . "If is a countable sequence of bounded subsets of a metrizable locally convex topological vector space then there exists a bounded subset of and a sequence of positive real numbers such that for all ."@en . . . . . . . . . . . "En analyse fonctionnelle et dans des domaines math\u00E9matiques reli\u00E9s, une partie d'un espace vectoriel topologique est dite born\u00E9e (au sens de von Neumann) si tout voisinage du vecteur nul peut \u00EAtre dilat\u00E9 de mani\u00E8re \u00E0 contenir cette partie. Ce concept a \u00E9t\u00E9 introduit par John von Neumann et Andre\u00EF Kolmogorov en 1935. Les parties born\u00E9es sont un moyen naturel de d\u00E9finir les (en) (localement convexes) sur les deux espaces vectoriels d'une paire duale."@fr . . . . . . . "Let be a set of continuous linear operators between two topological vector spaces and and let be any bounded subset of \nThen is uniformly bounded on if any of the following conditions are satisfied:\n# is equicontinuous.\n# is a convex compact Hausdorff subspace of and for every the orbit is a bounded subset of"@en . "Partie born\u00E9e d'un espace vectoriel topologique"@fr . . . "1124702385"^^ . . . . . . . . "Proposition"@en . . . . . . . "( \uC77C\uBC18\uC801\uC778 \uC720\uACC4 \uC9D1\uD569\uC5D0 \uAD00\uD574\uC11C\uB294 \uC720\uACC4 \uC9D1\uD569 \uBB38\uC11C\uB97C \uBCF4\uC2ED\uC2DC\uC624.) \uD568\uC218\uD574\uC11D\uD559\uACFC \uC218\uD559\uC758 \uAD00\uB828 \uBD84\uC57C\uC5D0\uC11C, \uC601\uBCA1\uD130\uC758 \uBAA8\uB4E0 \uADFC\uBC29\uC744 \uD33D\uCC3D\uC2DC\uCF1C\uC11C \uC704\uC0C1 \uBCA1\uD130 \uACF5\uAC04\uC758 \uC5B4\uB5A4 \uC9D1\uD569\uC744 \uD3EC\uD568\uD560 \uC218 \uC788\uC73C\uBA74 \uC720\uACC4 \uC9D1\uD569 \uB610\uB294 \uD3F0 \uB178\uC774\uB9CC \uC720\uACC4 \uC9D1\uD569\uC774\uB77C\uACE0 \uBD88\uB9B0\uB2E4. \uBC18\uB300\uB85C \uC9D1\uD569\uC774 \uC720\uACC4\uAC00 \uC544\uB2C8\uBA74 \uBB34\uACC4 \uC9D1\uD569\uC774\uB77C\uACE0 \uBD88\uB9B0\uB2E4. \uC720\uACC4 \uC9D1\uD569\uC758 \uC740 \uC808\uB300 \uBCFC\uB85D \uC9D1\uD569\uC774\uACE0 \uD761\uC218 \uC9D1\uD569\uC774\uAE30 \uB54C\uBB38\uC5D0, \uC720\uACC4\uC9D1\uD569\uC740 \uC778 \uC758 \uC744 \uC815\uC758\uD558\uB294 \uC77C\uBC18\uC801\uC778 \uBC29\uBC95\uC774\uB2E4. \uC774 \uAC1C\uB150\uC740 1935\uB144\uC5D0 \uC874 \uD3F0 \uB178\uC774\uB9CC\uACFC \uC548\uB4DC\uB808\uC774 \uCF5C\uBAA8\uACE0\uB85C\uD504\uC5D0 \uC758\uD574\uC11C \uCC98\uC74C\uC73C\uB85C \uB098\uD0C0\uB098\uAC8C \uB418\uC5C8\uB2E4."@ko . . . . "En analyse fonctionnelle et dans des domaines math\u00E9matiques reli\u00E9s, une partie d'un espace vectoriel topologique est dite born\u00E9e (au sens de von Neumann) si tout voisinage du vecteur nul peut \u00EAtre dilat\u00E9 de mani\u00E8re \u00E0 contenir cette partie. Ce concept a \u00E9t\u00E9 introduit par John von Neumann et Andre\u00EF Kolmogorov en 1935. Les parties born\u00E9es sont un moyen naturel de d\u00E9finir les (en) (localement convexes) sur les deux espaces vectoriels d'une paire duale."@fr . . . . . . . . "In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935."@en . . . .