[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11895#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11895","headline":"Borsuk-Vermutun  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Borsuk-Vermutun  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 Borsuk\u306e\u63a8\u5b9a \u30b8\u30aa\u30e1\u30c8\u30ea\u306e\u5206\u91ce\u304b\u3089\u306e\u6570\u5b66\u7684\u63a8\u5b9a\u3067\u3059\u3002\u305d\u308c\u306f\u3001\u5404\u90e8\u54c1\u304c\u975e\u5e38\u306b\u5c0f\u3055\u3044\u76f4\u5f84\u3092\u6301\u3064\u3088\u3046\u306b\u3001\u7279\u5b9a\u306e\u91cf\u306e\u9650\u3089\u308c\u305f\u76f4\u5f84\u3092\u5206\u89e3\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u90e8\u5206\u306e\u6570\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u3067\u3059\u3002 1933\u5e74\u306bKarol Borsuk\u304c\u63d0\u4f9b\u3057\u3001\u5f8c\u306b\u63d0\u4f9b\u3057\u305f\u8cea\u554f\u306f\u3001 n {displaystyle n} after-content-x4 \u5e38\u306b\u5bf8\u6cd5 n + \u521d\u3081 {displaystyle n+1} \u30b7\u30a7\u30a2\u300160\u5e74\u5f8c\u306b\u5426\u5b9a\u7684\u306b\u7b54\u3048\u3089\u308c\u307e\u3057\u305f\u3002 N\u6b21\u5143\u7a7a\u9593\u3067 after-content-x4 Rn{displaystyle mathbb","datePublished":"2022-06-25","dateModified":"2022-06-25","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?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\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/a601995d55609f2d9f5e233e36fbe9ea26011b3b","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/a601995d55609f2d9f5e233e36fbe9ea26011b3b","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11895","wordCount":2296,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 Borsuk\u306e\u63a8\u5b9a \u30b8\u30aa\u30e1\u30c8\u30ea\u306e\u5206\u91ce\u304b\u3089\u306e\u6570\u5b66\u7684\u63a8\u5b9a\u3067\u3059\u3002\u305d\u308c\u306f\u3001\u5404\u90e8\u54c1\u304c\u975e\u5e38\u306b\u5c0f\u3055\u3044\u76f4\u5f84\u3092\u6301\u3064\u3088\u3046\u306b\u3001\u7279\u5b9a\u306e\u91cf\u306e\u9650\u3089\u308c\u305f\u76f4\u5f84\u3092\u5206\u89e3\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u90e8\u5206\u306e\u6570\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u3067\u3059\u3002 1933\u5e74\u306bKarol Borsuk\u304c\u63d0\u4f9b\u3057\u3001\u5f8c\u306b\u63d0\u4f9b\u3057\u305f\u8cea\u554f\u306f\u3001 n {displaystyle n}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5e38\u306b\u5bf8\u6cd5 n + \u521d\u3081 {displaystyle n+1} \u30b7\u30a7\u30a2\u300160\u5e74\u5f8c\u306b\u5426\u5b9a\u7684\u306b\u7b54\u3048\u3089\u308c\u307e\u3057\u305f\u3002  N\u6b21\u5143\u7a7a\u9593\u3067        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Rn{displaystyle mathbb {r} ^{n}} \u76f4\u5f84\u3092\u4f7f\u7528\u3057\u3066\u3001\u591a\u304f\u306e\u30e6\u30fc\u30af\u30ea\u30b8\u30ab\u30eb\u6a19\u6e96\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059 \u3068 \u2282 Rn{displaystyle esubset mathbb {r} ^{n}} \u3044\u3064 \u3059\u3059\u308b { \u2016 \u30d0\u30c4  –  \u3068 \u2016 ; \u30d0\u30c4 \u3001 \u3068 \u2208 \u3068 } {displaystyle sup {| x-y |;\u3001x\u3001yin e}}} \uff08\u6570\u91cf\u306e2\u3064\u306e\u30dd\u30a4\u30f3\u30c8\u9593\u306e\u6700\u5927\u8ddd\u96e2\uff09\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002 \u3053\u308c\u3067\u91cf\u3092\u8a66\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3068 {displaystyle e} \u3057\u305f\u304c\u3063\u3066\u3001\u30b5\u30d6\u91cf\u3067 \u3068 = \u3068 1\u222a … \u222a \u3068 k{displaystyle e = e_ {1} cup ldots cup e_ {k}} \u305d\u308c\u305e\u308c\u306e\u90e8\u5206\u3092\u5206\u89e3\u3057\u307e\u3059 \u3068 i{displaystyle e_ {i}} \u3088\u308a\u5c0f\u3055\u306a\u76f4\u5f84 \u3068 {displaystyle e} \u3082\u3063\u3066\u3044\u308b\u3002\u554f\u984c\u306f\u3001\u30b5\u30d6\u91cf\u306e\u6570\u306e\u6570\u304c\u751f\u3058\u307e\u3059 \u3068 i{displaystyle e_ {i}} \u5fc5\u8981\u3067\u3059\u3002 \u901a\u5e38\u306eN\u6b21\u5143\u30b7\u30f3\u30d7\u30ec\u30c3\u30af\u30b9\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u5c11\u306a\u304f\u3068\u3082\u5c11\u306a\u304f\u3068\u3082 n + \u521d\u3081 {displaystyle n+1} \u306e\u305f\u3081\u306b\u5fc5\u8981\u306a\u6570\u91cf n + \u521d\u3081 {displaystyle n+1} \u30b3\u30fc\u30ca\u30fc\u306f\u3059\u3079\u3066\u3001\u76f4\u5f84\u306b\u7b49\u3057\u3044\u540c\u3058\u8ddd\u96e2\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u975e\u5e38\u306b\u5c0f\u3055\u3044\u76f4\u5f84\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306b\u306f\u6700\u59271\u3064\u306e\u30b3\u30fc\u30ca\u30fc\u3092\u542b\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u89d2\u304c\u3042\u308b\u306e\u3068\u540c\u3058\u304f\u3089\u3044\u5c11\u306a\u304f\u3068\u3082\u591a\u304f\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u304c\u5fc5\u8981\u3067\u3042\u308a\u3001\u6301\u3063\u3066\u3044\u307e\u3059\u3002 n + \u521d\u3081 {displaystyle n+1} \u3002\u5bf8\u6cd51.2\u30683\u306b\u3064\u3044\u3066\u306f\u660e\u3089\u304b\u306a\u3088\u3046\u306b\u3001\u3042\u306a\u305f\u306f\u5b9f\u969b\u306b\u30b7\u30f3\u30d7\u30ec\u30c3\u30af\u30b9\u3092\u5099\u3048\u3066\u3044\u307e\u3059 n + \u521d\u3081 {displaystyle n+1} \u79d1\u76ee\u3002 Karol Borsuk\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u3001\u5f7c\u304c\u5f3e\u4e38\u306e\u5206\u89e3\u3092\u6271\u3063\u305f\u300cN\u6b21\u5143\u570f\u306b\u95a2\u3059\u308b3\u3064\u306e\u6587\u7ae0\u300d\u3092\u9589\u3081\u307e\u3057\u305f\u3002 [\u521d\u3081] \uff1a \u6b21\u306e\u8cea\u554f\u306f\u958b\u3044\u305f\u307e\u307e\u3067\u3059\u3002 \u90e8\u5c4b\u306e\u9650\u3089\u308c\u305f\u30b5\u30d6\u30bb\u30c3\u30c8\u306f\u3059\u3079\u3066\u5b58\u5728\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059 Rn{displaystyle r^{n}} \uff08n+1\uff09\u306e\u91cf\u306e\u5206\u89e3\u91cf\u306f\u3001\u305d\u308c\u305e\u308c\u304cE\u3088\u308a\u3082\u76f4\u5f84\u304c\u5c0f\u3055\u3044\u3067\u3059\u304b\uff1f \u3053\u306e\u8cea\u554f\u3092\u65ad\u8a00\u3059\u3079\u304d\u3067\u3042\u308b\u3068\u3044\u3046\u4eee\u5b9a\u306f\u3001\u30dc\u30eb\u30b9\u30af\u306e\u63a8\u5b9a\u3068\u3057\u3066\u77e5\u3089\u308c\u300160\u5e74\u9593\u958b\u304b\u308c\u305f\u307e\u307e\u306b\u306a\u308a\u307e\u3057\u305f\u3002 \u90e8\u5c4b\u3067 R3{displaystyle mathbb {r} ^{3}} \u3053\u306e\u4eee\u5b9a\u306f1955\u5e74\u306b\u78ba\u8a8d\u3055\u308c\u307e\u3057\u305f\u3002 [2] \u3057\u305f\u304c\u3063\u3066\u3001\u9ad8\u6b21\u5143\u3067\u306e\u30dc\u30eb\u30b9\u30af\u306e\u5916\u89b3\u304c\u6b63\u3057\u304f\u306a\u3044\u3053\u3068\u304c\u5224\u660e\u3059\u308b\u306e\u306f\u9a5a\u304f\u3079\u304d\u3053\u3068\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002 1993\u5e74\u3001\u30b8\u30a7\u30d5\u30fb\u30ab\u30fc\u30f3\u3068G.\u30ab\u30e9\u30a4\u304c\u793a\u3057\u307e\u3057\u305f [3] \u305d\u308c\u306f\u5341\u5206\u306a\u5927\u304d\u306a\u5bf8\u6cd5\u306e\u305f\u3081\u3067\u3059 n {displaystyle n} \u5c11\u306a\u304f\u3068\u3082 \uff08 \u521d\u3081 \u3001 2 \uff09\uff09 n{displaystyle\uff081,2\uff09^{sqrt {n}}} \u30dc\u30eb\u30b9\u30af\u306e\u5916\u89b3\u304c\u53cd\u8ad6\u3055\u308c\u305f\u30b5\u30d6\u30bb\u30c3\u30c8\u304c\u5fc5\u8981\u3067\u3057\u305f\u3002 \uff08 \u521d\u3081 \u3001 2 \uff09\uff09 n{displaystyle\uff081,2\uff09^{sqrt {n}}} \u3088\u308a\u901f\u304f\u6210\u9577\u3057\u307e\u3059 n + \u521d\u3081 {displaystyle n+1} \u3002 964\u6b21\u5143\u7a7a\u9593\u3067A. nilli\u306b\u3088\u3063\u3066\u5177\u4f53\u7684\u306a\u53cd\u4f8b\u304c\u767a\u898b\u3055\u308c\u307e\u3057\u305f [4] \u3001\u305d\u306e\u5f8c\u3001298\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308bA.\u30d2\u30f3\u30ea\u30c3\u30d2\u30b9\u3068C.\u30ea\u30d2\u30bf\u30fc\u306b\u3088\u308b\u5225\u306e\u5225\u306e\u3082\u306e\u3002 [5] \u4eca\u65e5\u300164\u306e\u5bf8\u6cd5\u306e\u30dc\u30eb\u30b9\u30af\u306e\u63a8\u5b9a\u304c\u9593\u9055\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002 [6] [7] Borsuk\u306e\u63a8\u5b9a\u304c\u3082\u306f\u3084\u30aa\u30fc\u30d7\u30f3\u3067\u306f\u306a\u3044\u6700\u5c0f\u306e\u6b21\u5143\u306e\u554f\u984c\u3002 \u2191  K. BORSUK\uff1a N\u6b21\u5143\u7403\u306b\u95a2\u3059\u308b3\u3064\u306e\u6587 \uff08PDF; 1.1 MB\uff09 \u3001\u57fa\u672c\u7684\u306aMathematica\uff081933\uff09\u3001\u7b2c20\u5dfb\u3001177\u301c190\u30da\u30fc\u30b8  \u2191  H. G.\u30a8\u30b0\u30eb\u30b9\u30c8\u30f3\uff1a \u76f4\u5f84\u304c\u5c0f\u3055\u3044\u30bb\u30c3\u30c8\u30673\u6b21\u5143\u30bb\u30c3\u30c8\u3092\u30ab\u30d0\u30fc\u3057\u307e\u3059 \u3001J\u3002\u30ed\u30f3\u30c9\u30f3\u6570\u5b66\u5354\u4f1a\uff081955\uff09\u3001\u7b2c30\u5dfb\u300111\u301c24\u30da\u30fc\u30b8  \u2191  \u30ab\u30fc\u30f3\u3001\u526f \u30dc\u30eb\u30b5\u30af\u306e\u63a8\u6e2c\u3078\u306e\u53cd\u4f8b \u3001Bulletin American Mathematical Society\u3001bd\u3002 29\u30011993\u3001S\u300260\u201362  \u2191  A.\u30cb\u30ea\uff1a Borsuk\u306e\u554f\u984c\u306b\u3064\u3044\u3066 \u3001\u30a8\u30eb\u30b5\u30ec\u30e0\u30b3\u30f3\u30d3\u30ca\u30c8\u30ea\u30af\u30b9’93\u3001Contemporary Mathematics 178\u3001AMS 1994\u3001Seiten 209\u2013210  \u2191  A.\u30d2\u30f3\u30ea\u30c3\u30d2\u3068C.\u30ea\u30d2\u30bf\u30fc\uff1a \u30dc\u30eb\u30af\u6570\u304c\u591a\u3044\u65b0\u3057\u3044\u30bb\u30c3\u30c8 \u3001\u30c7\u30a3\u30b9\u30af\u30ea\u30fc\u30c8\u6570\u5b66\uff082003\uff09\u3001\u7b2c270\u5dfb\u3001137\u301c147\u30da\u30fc\u30b8  \u2191  Andriy V. Bondarenko\uff1a Borsuk\u306e2\u8ddd\u96e2\u30bb\u30c3\u30c8\u306e\u63a8\u6e2c\u306b\u3064\u3044\u3066  \u2191  \u30c8\u30fc\u30de\u30b9\u30fb\u30b8\u30a7\u30f3\u30ea\u30c3\u30c1\uff1a Borsuk\u306e\u63a8\u6e2c\u306b\u5bfe\u3059\u308b64\u6b21\u5143\u306e2\u6b21\u5143\u306e\u53cd\u4f8b        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/11895#breadcrumbitem","name":"Borsuk-Vermutun  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]