. "En matem\u00E1ticas, el \u00C1lgebra de Cantor es un seg\u00FAn la operaci\u00F3n aditiva de uni\u00F3n y multiplicativa de intersecci\u00F3n, puesto que para estas leyes de composici\u00F3n interna se cumplen las propiedades conmutativa y asociativa; sin embargo, no es un grupo puesto que las ecuaciones , no poseen soluciones; por ejemplo, para el caso en que los conjuntos no se intersequen: . Por consiguiente, el \u00E1lgebra de Cantor seg\u00FAn las operaci\u00F3n bin\u00E1dicas de uni\u00F3n e intersecci\u00F3n de conjuntos no es un anillo. Esta \u00E1lgebra pertenece a otra clase de \u00E1lgebras fundamentales, o sea a la clase de ret\u00EDculos."@es . . . . . "Cantor algebra"@en . . . . . . . . "En matem\u00E1ticas, el \u00C1lgebra de Cantor es un seg\u00FAn la operaci\u00F3n aditiva de uni\u00F3n y multiplicativa de intersecci\u00F3n, puesto que para estas leyes de composici\u00F3n interna se cumplen las propiedades conmutativa y asociativa; sin embargo, no es un grupo puesto que las ecuaciones , no poseen soluciones; por ejemplo, para el caso en que los conjuntos no se intersequen: . Por consiguiente, el \u00E1lgebra de Cantor seg\u00FAn las operaci\u00F3n bin\u00E1dicas de uni\u00F3n e intersecci\u00F3n de conjuntos no es un anillo. Esta \u00E1lgebra pertenece a otra clase de \u00E1lgebras fundamentales, o sea a la clase de ret\u00EDculos."@es . . . "\u00C1lgebra de Cantor"@es . "In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete. The countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable number of generators. Up to isomorphism, this is the only nontrivial Boolean algebra that is both countable and atomless. The complete Cantor algebra is the complete Boolean algebra of Borel subsets of the reals modulo meager sets. It is isomorphic to the completion of the countable Cantor algebra. (The complete Cantor algebra is sometimes called the Cohen algebra, though \"Cohen algebra\" usually refers to a different type of Boolean algebra.) The complete Cantor algebra was studied by von Neumann in 1935 (later published as), who showed that it is not isomorphic to the random algebra of Borel subsets modulo measure zero sets."@en . . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u30B2\u30AA\u30EB\u30AF\u30FB\u30AB\u30F3\u30C8\u30FC\u30EB\u306B\u3061\u306A\u3093\u3067\u540D\u3065\u3051\u3089\u308C\u305F\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570 (Cantor algebra) \u306F2\u3064\u306E\u95A2\u9023\u304C\u6DF1\u3044\u30D6\u30FC\u30EB\u4EE3\u6570\u306E\u4E00\u65B9\u3067\u3042\u308B\u30021\u3064\u306F\u53EF\u7B97\u6027\u3067\u3001\u3082\u30461\u3064\u306F\u5B8C\u5099\u6027\u3067\u3042\u308B\u3002 \u53EF\u7B97\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F\u30AB\u30F3\u30C8\u30FC\u30EB\u96C6\u5408\u306E\u3059\u3079\u3066\u306E\u958B\u304B\u3064\u9589\u306A\u90E8\u5206\u96C6\u5408\u304B\u3089\u306A\u308B\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u3042\u308B\u3002\u3053\u308C\u306F\u53EF\u7B97\u500B\u306E\u751F\u6210\u5143\u4E0A\u306E\u81EA\u7531\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u3042\u308B\u3002\u540C\u578B\u3092\u9664\u3044\u3066\u3001\u3053\u308C\u306F\u53EF\u7B97\u304B\u3064 atomless \u306A\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u975E\u81EA\u660E\u306A\u552F\u4E00\u306E\u3082\u306E\u3067\u3042\u308B\u3002 \u5B8C\u5099\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F\u3092\u6CD5\u3068\u3057\u305F\u5B9F\u6570\u306E\u30DC\u30EC\u30EB\u90E8\u5206\u96C6\u5408\u306E\u5B8C\u5099\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u3042\u308B\u3002\u3053\u308C\u306F\u53EF\u7B97\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306E\u5B8C\u5099\u5316\u306B\u540C\u578B\u3067\u3042\u308B\u3002\u5B8C\u5099\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F\u3001\u30B3\u30FC\u30A8\u30F3\u4EE3\u6570\u3068\u547C\u3070\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u304C\u3001\u300C\u30B3\u30FC\u30A8\u30F3\u4EE3\u6570\u300D\u306F\u901A\u5E38\u5225\u306E\u30BF\u30A4\u30D7\u306E\u30D6\u30FC\u30EB\u4EE3\u6570\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u5B8C\u5099\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F1935\u5E74\u306B\u30D5\u30A9\u30F3\u30FB\u30CE\u30A4\u30DE\u30F3\u306B\u3088\u3063\u3066\u7814\u7A76\u3055\u308C\u3001\u306E\u3061\u306B\u3068\u3057\u3066\u51FA\u7248\u3055\u308C\u305F\u3002\u5F7C\u306F\u305D\u308C\u304C\u6E2C\u5EA60\u306E\u96C6\u5408\u3092\u6CD5\u3068\u3057\u305F\u30DC\u30EC\u30EB\u90E8\u5206\u96C6\u5408\u306E\u306B\u540C\u578B\u3067\u306A\u3044\u3053\u3068\u3092\u793A\u3057\u305F\u3002"@ja . . . "964117540"^^ . "\u6570\u5B66\u306B\u304A\u3044\u3066\u3001\u30B2\u30AA\u30EB\u30AF\u30FB\u30AB\u30F3\u30C8\u30FC\u30EB\u306B\u3061\u306A\u3093\u3067\u540D\u3065\u3051\u3089\u308C\u305F\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570 (Cantor algebra) \u306F2\u3064\u306E\u95A2\u9023\u304C\u6DF1\u3044\u30D6\u30FC\u30EB\u4EE3\u6570\u306E\u4E00\u65B9\u3067\u3042\u308B\u30021\u3064\u306F\u53EF\u7B97\u6027\u3067\u3001\u3082\u30461\u3064\u306F\u5B8C\u5099\u6027\u3067\u3042\u308B\u3002 \u53EF\u7B97\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F\u30AB\u30F3\u30C8\u30FC\u30EB\u96C6\u5408\u306E\u3059\u3079\u3066\u306E\u958B\u304B\u3064\u9589\u306A\u90E8\u5206\u96C6\u5408\u304B\u3089\u306A\u308B\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u3042\u308B\u3002\u3053\u308C\u306F\u53EF\u7B97\u500B\u306E\u751F\u6210\u5143\u4E0A\u306E\u81EA\u7531\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u3042\u308B\u3002\u540C\u578B\u3092\u9664\u3044\u3066\u3001\u3053\u308C\u306F\u53EF\u7B97\u304B\u3064 atomless \u306A\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u975E\u81EA\u660E\u306A\u552F\u4E00\u306E\u3082\u306E\u3067\u3042\u308B\u3002 \u5B8C\u5099\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F\u3092\u6CD5\u3068\u3057\u305F\u5B9F\u6570\u306E\u30DC\u30EC\u30EB\u90E8\u5206\u96C6\u5408\u306E\u5B8C\u5099\u30D6\u30FC\u30EB\u4EE3\u6570\u3067\u3042\u308B\u3002\u3053\u308C\u306F\u53EF\u7B97\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306E\u5B8C\u5099\u5316\u306B\u540C\u578B\u3067\u3042\u308B\u3002\u5B8C\u5099\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F\u3001\u30B3\u30FC\u30A8\u30F3\u4EE3\u6570\u3068\u547C\u3070\u308C\u308B\u3053\u3068\u304C\u3042\u308B\u304C\u3001\u300C\u30B3\u30FC\u30A8\u30F3\u4EE3\u6570\u300D\u306F\u901A\u5E38\u5225\u306E\u30BF\u30A4\u30D7\u306E\u30D6\u30FC\u30EB\u4EE3\u6570\u306E\u3053\u3068\u3067\u3042\u308B\u3002\u5B8C\u5099\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570\u306F1935\u5E74\u306B\u30D5\u30A9\u30F3\u30FB\u30CE\u30A4\u30DE\u30F3\u306B\u3088\u3063\u3066\u7814\u7A76\u3055\u308C\u3001\u306E\u3061\u306B\u3068\u3057\u3066\u51FA\u7248\u3055\u308C\u305F\u3002\u5F7C\u306F\u305D\u308C\u304C\u6E2C\u5EA60\u306E\u96C6\u5408\u3092\u6CD5\u3068\u3057\u305F\u30DC\u30EC\u30EB\u90E8\u5206\u96C6\u5408\u306E\u306B\u540C\u578B\u3067\u306A\u3044\u3053\u3068\u3092\u793A\u3057\u305F\u3002"@ja . . . "2041"^^ . . . . . "\u30AB\u30F3\u30C8\u30FC\u30EB\u4EE3\u6570"@ja . "In mathematics, a Cantor algebra, named after Georg Cantor, is one of two closely related Boolean algebras, one countable and one complete. The countable Cantor algebra is the Boolean algebra of all clopen subsets of the Cantor set. This is the free Boolean algebra on a countable number of generators. Up to isomorphism, this is the only nontrivial Boolean algebra that is both countable and atomless."@en . . . . . . "43215632"^^ . . .