[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4927#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4927","headline":"\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406 – Wikipedia","name":"\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406 – Wikipedia","description":"\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u30d6\u30fc\u30eb\u4ee3\u6570\u306b\u5bfe\u3059\u308b\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406\uff08\u30b9\u30c8\u30fc\u30f3\u306e\u3072\u3087\u3046\u3052\u3093\u3066\u3044\u308a\u3001\u82f1: Stone’s representation theorem\uff09\u306f\u3001\u4efb\u610f\u306e\u30d6\u30fc\u30eb\u4ee3\u6570\u304c\u4f55\u3089\u304b\u306e\u96c6\u5408\u4ee3\u6570 (field of sets) \u306b\u540c\u578b\u3067\u3042\u308b\u3053\u3068\u3092\u8ff0\u3079\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u306e\u5b9a\u7406\u306f20\u4e16\u7d00\u524d\u534a\u306b\u6d6e\u4e0a\u3057\u3066\u304d\u305f\u30d6\u30fc\u30eb\u4ee3\u6570\u306e\u6df1\u3044\u7406\u89e3\u306b\u3068\u3063\u3066\u57fa\u672c\u7684\u3067\u3042\u308b\u3002\u3053\u306e\u5b9a\u7406\u3092\u521d\u3081\u3066\u8a3c\u660e\u3057\u305f\u306e\u306f Stone (1936) \u3067\u3042\u308a\u3001\u540d\u79f0\u306f\u3053\u306e\u696d\u7e3e\u306b\u56e0\u3080\u3082\u306e\u3067\u3042\u308b\u3002\u30b9\u30c8\u30fc\u30f3\u306f\u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u4e0a\u306e\u4f5c\u7528\u7d20\u306e\u30b9\u30da\u30af\u30c8\u30eb\u8ad6\u306e\u7814\u7a76\u306b\u3088\u3063\u3066\u3053\u306e\u5b9a\u7406\u3092\u5c0e\u3044\u305f\u3002 \u3053\u306e\u5b9a\u7406\u306f\u30b9\u30c8\u30fc\u30f3\u53cc\u5bfe\u6027\u306e\u7279\u6b8a\u306a\u5834\u5408\u306b\u5f53\u305f\u308b\u3002 Table of Contents \u30b9\u30c8\u30fc\u30f3\u7a7a\u9593[\u7de8\u96c6]\u8868\u73fe\u5b9a\u7406[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6] \u30b9\u30c8\u30fc\u30f3\u7a7a\u9593[\u7de8\u96c6] \u5404\u30d6\u30fc\u30eb\u4ee3\u6570 B \u306f\u3001\u305d\u308c\u306b\u4ed8\u968f\u3059\u308b\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593\u3068\u547c\u3070\u308c\u308b\u4f4d\u76f8\u7a7a\u9593","datePublished":"2021-05-31","dateModified":"2021-05-31","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d664c903dc18fef36f580dfd8320f0f684c3657f","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d664c903dc18fef36f580dfd8320f0f684c3657f","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4927","about":["Wiki"],"wordCount":999,"articleBody":"\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u30d6\u30fc\u30eb\u4ee3\u6570\u306b\u5bfe\u3059\u308b\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406\uff08\u30b9\u30c8\u30fc\u30f3\u306e\u3072\u3087\u3046\u3052\u3093\u3066\u3044\u308a\u3001\u82f1: Stone’s representation theorem\uff09\u306f\u3001\u4efb\u610f\u306e\u30d6\u30fc\u30eb\u4ee3\u6570\u304c\u4f55\u3089\u304b\u306e\u96c6\u5408\u4ee3\u6570 (field of sets) \u306b\u540c\u578b\u3067\u3042\u308b\u3053\u3068\u3092\u8ff0\u3079\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u306e\u5b9a\u7406\u306f20\u4e16\u7d00\u524d\u534a\u306b\u6d6e\u4e0a\u3057\u3066\u304d\u305f\u30d6\u30fc\u30eb\u4ee3\u6570\u306e\u6df1\u3044\u7406\u89e3\u306b\u3068\u3063\u3066\u57fa\u672c\u7684\u3067\u3042\u308b\u3002\u3053\u306e\u5b9a\u7406\u3092\u521d\u3081\u3066\u8a3c\u660e\u3057\u305f\u306e\u306f Stone (1936) \u3067\u3042\u308a\u3001\u540d\u79f0\u306f\u3053\u306e\u696d\u7e3e\u306b\u56e0\u3080\u3082\u306e\u3067\u3042\u308b\u3002\u30b9\u30c8\u30fc\u30f3\u306f\u30d2\u30eb\u30d9\u30eb\u30c8\u7a7a\u9593\u4e0a\u306e\u4f5c\u7528\u7d20\u306e\u30b9\u30da\u30af\u30c8\u30eb\u8ad6\u306e\u7814\u7a76\u306b\u3088\u3063\u3066\u3053\u306e\u5b9a\u7406\u3092\u5c0e\u3044\u305f\u3002  \u3053\u306e\u5b9a\u7406\u306f\u30b9\u30c8\u30fc\u30f3\u53cc\u5bfe\u6027\u306e\u7279\u6b8a\u306a\u5834\u5408\u306b\u5f53\u305f\u308b\u3002Table of Contents\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593[\u7de8\u96c6]\u8868\u73fe\u5b9a\u7406[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593[\u7de8\u96c6]\u5404\u30d6\u30fc\u30eb\u4ee3\u6570 B \u306f\u3001\u305d\u308c\u306b\u4ed8\u968f\u3059\u308b\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593\u3068\u547c\u3070\u308c\u308b\u4f4d\u76f8\u7a7a\u9593 S(B) \u3092\u6301\u3064\u3002S(B) \u306b\u304a\u3051\u308b\u70b9\u306f B \u4e0a\u306e\u8d85\u30d5\u30a3\u30eb\u30bf\u30fc\u3001\u3042\u308b\u3044\u306f\u540c\u3058\u3053\u3068\u3060\u304c B \u304b\u3089\u4e8c\u5143\u30d6\u30fc\u30eb\u4ee3\u6570\u3078\u306e\u6e96\u540c\u578b\u3067\u3042\u308b\u3002S(B) \u306b\u304a\u3051\u308b\u4f4d\u76f8\u306f B \u306e\u5143 b \u306b\u5bfe\u3057\u3066  {x\u2208S(B)\u2223b\u2208x}{displaystyle {xin S(B)mid bin x}}\u306a\u308b\u5f62\u306b\u66f8\u3051\u308b\u96c6\u5408\u5168\u4f53\u304b\u3089\u306a\u308b\u57fa\u5e95\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u3002\u4efb\u610f\u306e\u30d6\u30fc\u30eb\u4ee3\u6570 B \u306b\u5bfe\u3057 S(B) \u306f\u30b3\u30f3\u30d1\u30af\u30c8\u5b8c\u5168\u4e0d\u9023\u7d50\u30cf\u30a6\u30b9\u30c9\u30eb\u30d5\u7a7a\u9593\u3067\u3042\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u4f4d\u76f8\u7a7a\u9593\u306f\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593\uff08\u307e\u305f\u306f\u526f\u6709\u9650\u7a7a\u9593 (profinite spaces)\uff09\u3068\u547c\u3070\u308c\u308b\u3002\u9006\u306b\u3001\u4efb\u610f\u306e\u4f4d\u76f8\u7a7a\u9593 X \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001X \u306e\u958b\u304b\u3064\u9589\u96c6\u5408\u5168\u4f53\u306e\u6210\u3059\u65cf\u306f\u30d6\u30fc\u30eb\u4ee3\u6570\u306b\u306a\u308b\u3002\u8868\u73fe\u5b9a\u7406[\u7de8\u96c6]\u5358\u7d14\u7248\u306e\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406\u306f\u3001\u4efb\u610f\u306e\u30d6\u30fc\u30eb\u4ee3\u6570 B \u304c\u4ed8\u968f\u3059\u308b\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593 S(B) \u306e\u958b\u304b\u3064\u9589\u90e8\u5206\u96c6\u5408\u5168\u4f53\u306e\u6210\u3059\u96c6\u5408\u4ee3\u6570\u306b\u540c\u578b\u3067\u3042\u308b\u3068\u3044\u3046\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u306e\u540c\u578b\u5199\u50cf\u306f B \u306e\u5143 b \u3092 b \u3092\u542b\u3080\u8d85\u30d5\u30a3\u30eb\u30bf\u30fc\u5168\u4f53\u306e\u6210\u3059\u96c6\u5408\uff08\u3053\u306e\u96c6\u5408\u306f S(B) \u306e\u4f4d\u76f8\u306e\u9078\u3073\u65b9\u3068 B \u304c\u30d6\u30fc\u30eb\u4ee3\u6570\u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001\u958b\u304b\u3064\u9589\u306b\u306a\u308b\uff09\u3078\u5199\u3059\u3002  \u5b9a\u7406\u3092\u570f\u8ad6\u306e\u8a00\u8449\u3092\u7528\u3044\u3066\u66f8\u304d\u76f4\u3059\u3068\u3001\u30d6\u30fc\u30eb\u4ee3\u6570\u306e\u570f\u3068\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593\u306e\u570f\u306e\u9593\u306b\u53cc\u5bfe\u6027\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3082\u306e\u306b\u306a\u308b\u3002\u3053\u306e\u53cc\u5bfe\u6027\u306f\u30d6\u30fc\u30eb\u4ee3\u6570\u3068\u305d\u306e\u30b9\u30c8\u30fc\u30f3\u7a7a\u9593\u306e\u9593\u306b\u540c\u578b\u304c\u3042\u308b\u3053\u3068\u306b\u52a0\u3048\u3066\u305d\u306e\u540c\u578b\u304c\u51fd\u624b\u7684\u3067\u3042\u308b\u3053\u3068\u3001\u5373\u3061\u30d6\u30fc\u30eb\u4ee3\u6570 A \u304b\u3089\u5225\u306e\u30d6\u30fc\u30eb\u4ee3\u6570 B \u3078\u306e\u5404\u6e96\u540c\u578b\u306b\u5bfe\u3057\u3066\u3001S(B) \u304b\u3089 S(A) \u3078\u306e\u9023\u7d9a\u51fd\u6570\u304c\u81ea\u7136\u306a\u5bfe\u5fdc\u3092\u6301\u3064\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u305d\u308c\u3089\u306e\u570f\u306e\u9593\u306b\u570f\u540c\u5024\u3092\u4e0e\u3048\u308b\u53cd\u5909\u51fd\u624b\u304c\u5b58\u5728\u3059\u308b\u306e\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u570f\u306e\u975e\u81ea\u660e\u306a\u53cc\u5bfe\u6027\u306e\u521d\u671f\u306e\u4f8b\u3067\u3042\u308b\u3002\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406\u306f\u3001\u3082\u3063\u3068\u4e00\u822c\u306e\u5834\u5408\u3067\u306f\u4f4d\u76f8\u7a7a\u9593\u3068\u534a\u9806\u5e8f\u96c6\u5408\u3068\u306e\u9593\u306e\u53cc\u5bfe\u6027\u3092\u6271\u3046\u67a0\u7d44\u307f\u3092\u4e0e\u3048\u308b\u3001\u30b9\u30c8\u30fc\u30f3\u53cc\u5bfe\u6027\u306e\u7279\u5225\u306e\u5834\u5408\u3067\u3042\u308b\u3002\u305d\u306e\u8a3c\u660e\u306b\u306f\u9078\u629e\u516c\u7406\u307e\u305f\u306f\u305d\u306e\u5f31\u3044\u5f62\u306e\u516c\u7406\u3092\u5fc5\u8981\u3068\u3059\u308b\u3002\u7279\u306b\u3053\u306e\u5b9a\u7406\u306f\u3001\u4efb\u610f\u306e\u30d6\u30fc\u30eb\u4ee3\u6570\u304c\u7d20\u30a4\u30c7\u30a2\u30eb\u3092\u6301\u3064\u3053\u3068\u3092\u8ff0\u3079\u305f\u5f31\u3044\u5f62\u306e\u9078\u629e\u539f\u7406\u3067\u3042\u308b\u30d6\u30fc\u30eb\u7d20\u30a4\u30c7\u30a2\u30eb\u5b9a\u7406\u3068\u540c\u5024\u306b\u306a\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Halmos, Paul; Givant, Steven (1998), Logic as Algebra, Dolciani Mathematical Expositions No. 21, The Mathematical Association of America\u00a0Peter T., Johnstone (1982), Stone Spaces, Cambridge University Press, ISBN\u00a00-521-23893-5\u00a0H. Stone, Marshall (1936), The Theory of Representations of Boolean Algebras, Transactions of the American Mathematical Society 40, http:\/\/links.jstor.org\/sici?sici=0002-9947%28193607%2940%3A1%3C37%3ATTORFB%3E2.0.CO%3B2-8\u00a0\u30aa\u30f3\u30e9\u30a4\u30f3\u516c\u958b\u306e\u30e2\u30ce\u30b0\u30e9\u30d5:"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki7\/archives\/4927#breadcrumbitem","name":"\u30b9\u30c8\u30fc\u30f3\u306e\u8868\u73fe\u5b9a\u7406 – Wikipedia"}}]}]