[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/119712#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/119712","headline":"\u6709\u754c – Wikipedia","name":"\u6709\u754c – Wikipedia","description":"\u4e0a\u304c\u6709\u754c\u96c6\u5408\u3001\u4e0b\u304c\u975e\u6709\u754c\u96c6\u5408\u3092\u6a21\u5f0f\u7684\u306b\u8868\u3057\u305f\u3082\u306e\u3002\u305f\u3060\u3057\u3001\u4e0b\u306e\u307b\u3046\u306f\u67a0\u3092\u8d85\u3048\u3066\u53f3\u65b9\u3078\u5ef6\u3005\u3068\u7d9a\u304f\u3082\u306e\u3068\u3059\u308b\u3002 \u6570\u5b66\u306b\u304a\u3044\u3066\u96c6\u5408\u304c\u6709\u754c\uff08\u3086\u3046\u304b\u3044\u3001\u82f1: bounded\uff09\u3067\u3042\u308b\u3001\u307e\u305f\u306f\u6709\u754c\u96c6\u5408\uff08\u3086\u3046\u304b\u3044\u3057\u3085\u3046\u3054\u3046\u3001bounded set\uff09\u3067\u3042\u308b\u3068\u306f\u3001\u3042\u308b\u7a2e\u306e\u300c\u5dee\u6e21\u3057\u306e\u5927\u304d\u3055\u300d\u306b\u95a2\u3059\u308b\u6709\u9650\u6027\u3092\u305d\u308c\u304c\u6301\u3064\u3068\u304d\u306b\u3044\u3046\u3002\u6709\u754c\u3067\u306a\u3044\u96c6\u5408\u306f\u975e\u6709\u754c\uff08\u3072\u3086\u3046\u304b\u3044\u3001unbounded\uff09\u3067\u3042\u308b\u3068\u3044\u3046\u3002 \u5358\u7d14\u9589\u66f2\u7dda\u306f\u305d\u308c\u3092\u5883\u754c\u3068\u3057\u3066\u5e73\u9762 R2 \u3092\u6709\u754c\uff08\u5185\u5074\uff09\u304a\u3088\u3073\u975e\u6709\u754c\uff08\u5916\u5074\uff09\u306a\u4e8c\u3064\u306e\u9818\u57df\u306b\u5206\u3051\u308b\u3002 Table of Contents \u9806\u5e8f\u96c6\u5408\u306e\u6709\u754c\u6027[\u7de8\u96c6]\u8ddd\u96e2\u7a7a\u9593\u306e\u6709\u754c\u6027[\u7de8\u96c6]\u4f8b\u3068\u6027\u8cea[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6] \u9806\u5e8f\u96c6\u5408\u306e\u6709\u754c\u6027[\u7de8\u96c6] \u9806\u5e8f\u96c6\u5408 (X, \u2264) \u3068\u305d\u306e\u7a7a\u3067\u306a\u3044\u90e8\u5206\u96c6\u5408 A \u3092\u8003\u3048\u308b\u3002X \u306e\u5143 L","datePublished":"2022-03-18","dateModified":"2022-03-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/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:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/06\/Bounded_unbounded.svg\/250px-Bounded_unbounded.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/06\/Bounded_unbounded.svg\/250px-Bounded_unbounded.svg.png","height":"284","width":"250"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/119712","about":["Wiki"],"wordCount":726,"articleBody":" \u4e0a\u304c\u6709\u754c\u96c6\u5408\u3001\u4e0b\u304c\u975e\u6709\u754c\u96c6\u5408\u3092\u6a21\u5f0f\u7684\u306b\u8868\u3057\u305f\u3082\u306e\u3002\u305f\u3060\u3057\u3001\u4e0b\u306e\u307b\u3046\u306f\u67a0\u3092\u8d85\u3048\u3066\u53f3\u65b9\u3078\u5ef6\u3005\u3068\u7d9a\u304f\u3082\u306e\u3068\u3059\u308b\u3002\u6570\u5b66\u306b\u304a\u3044\u3066\u96c6\u5408\u304c\u6709\u754c\uff08\u3086\u3046\u304b\u3044\u3001\u82f1: bounded\uff09\u3067\u3042\u308b\u3001\u307e\u305f\u306f\u6709\u754c\u96c6\u5408\uff08\u3086\u3046\u304b\u3044\u3057\u3085\u3046\u3054\u3046\u3001bounded set\uff09\u3067\u3042\u308b\u3068\u306f\u3001\u3042\u308b\u7a2e\u306e\u300c\u5dee\u6e21\u3057\u306e\u5927\u304d\u3055\u300d\u306b\u95a2\u3059\u308b\u6709\u9650\u6027\u3092\u305d\u308c\u304c\u6301\u3064\u3068\u304d\u306b\u3044\u3046\u3002\u6709\u754c\u3067\u306a\u3044\u96c6\u5408\u306f\u975e\u6709\u754c\uff08\u3072\u3086\u3046\u304b\u3044\u3001unbounded\uff09\u3067\u3042\u308b\u3068\u3044\u3046\u3002 \u5358\u7d14\u9589\u66f2\u7dda\u306f\u305d\u308c\u3092\u5883\u754c\u3068\u3057\u3066\u5e73\u9762 R2 \u3092\u6709\u754c\uff08\u5185\u5074\uff09\u304a\u3088\u3073\u975e\u6709\u754c\uff08\u5916\u5074\uff09\u306a\u4e8c\u3064\u306e\u9818\u57df\u306b\u5206\u3051\u308b\u3002Table of Contents\u9806\u5e8f\u96c6\u5408\u306e\u6709\u754c\u6027[\u7de8\u96c6]\u8ddd\u96e2\u7a7a\u9593\u306e\u6709\u754c\u6027[\u7de8\u96c6]\u4f8b\u3068\u6027\u8cea[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u9806\u5e8f\u96c6\u5408\u306e\u6709\u754c\u6027[\u7de8\u96c6]\u9806\u5e8f\u96c6\u5408 (X, \u2264) \u3068\u305d\u306e\u7a7a\u3067\u306a\u3044\u90e8\u5206\u96c6\u5408 A \u3092\u8003\u3048\u308b\u3002X \u306e\u5143 L \u304c\u3001A \u306e\u4efb\u610f\u306e\u5143 a \u306b\u3064\u3044\u3066 a \u2264 L \u3092\u6e80\u305f\u3059\u3068\u304d\u3001L \u3092 A \u306e\u4e0a\u754c (upper bound) \u3068\u3044\u3044\u3001\u4e0a\u754c\u3092\u6301\u3064 A \u306f\u4e0a\u306b\u6709\u754c\u3067\u3042\u308b\u307e\u305f\u306f\u300c\u4e0a\u304b\u3089\u6291\u3048\u3089\u308c\u308b\u300d(bounded [from] above) \u3068\u3044\u3046\u3002\u307e\u305f X \u306e\u5143 l \u304c\u3001A \u306e\u4efb\u610f\u306e\u5143 a \u306b\u3064\u3044\u3066 l \u2264 a \u3092\u6e80\u305f\u3059\u306a\u3089\u3070\u3001l \u3092 A \u306e\u4e0b\u754c (lower bound) \u3068\u3044\u3044\u3001\u4e0b\u754c\u3092\u6301\u3064 A \u306f\u4e0b\u306b\u6709\u754c\u3067\u3042\u308b\u3001\u307e\u305f\u306f\u300c\u4e0b\u304b\u3089\u62bc\u3055\u3048\u3089\u308c\u308b\u300d(bounded [from] below) \u3068\u3044\u3046\u3002 \u4e0a\u306b\u6709\u754c\u304b\u3064\u4e0b\u306b\u6709\u754c\u306a\u96c6\u5408\u306f\u5358\u306b\u6709\u754c\u3067\u3042\u308b\u3068\u3044\u3046\u3002\u9806\u5e8f\u96c6\u5408 (X, \u2264) \u304c\u534a\u9806\u5e8f \u2264 \u306b\u95a2\u3057\u3066\u6700\u5927\u5143\u304a\u3088\u3073\u6700\u5c0f\u5143\u3092\u6301\u3064\u306a\u3089\u3070\u3001\u3053\u306e\u534a\u9806\u5e8f\u306f\u6709\u754c\u9806\u5e8f (bounded order) \u3067\u3042\u308b\u3001\u307e\u305f\u306f X \u306f\u6709\u754c\u9806\u5e8f\u96c6\u5408 (bounded poset) \u3067\u3042\u308b\u3068\u3044\u3046\u3002\u6709\u754c\u9806\u5e8f\u3092\u6301\u3064\u9806\u5e8f\u96c6\u5408 X \u306b\u5bfe\u3057\u3001\u90e8\u5206\u96c6\u5408 S \u306b\u9806\u5e8f\u3092\u5236\u9650\u3057\u305f (S, \u2264) \u306f\u5fc5\u305a\u3057\u3082\u6709\u754c\u9806\u5e8f\u306b\u306f\u306a\u3089\u306a\u3044\u3002\u8ddd\u96e2\u7a7a\u9593\u306e\u6709\u754c\u6027[\u7de8\u96c6]\u8ddd\u96e2\u7a7a\u9593 (M, d) \u306e\u90e8\u5206\u96c6\u5408 S \u304c\u6709\u754c\u3067\u3042\u308b\u3068\u306f\u3001S \u304c\u6709\u9650\u306a\u534a\u5f84\u3092\u6301\u3064\u7403\u3067\u8986\u3048\u308b\u3053\u3068\u3092\u3044\u3046\u3002\u3059\u306a\u308f\u3061\u3001M \u306e\u5143 x \u3068\u6b63\u6570 r > 0 \u3067\u3001\u4efb\u610f\u306e S \u306e\u5143 s \u306b\u5bfe\u3057\u3066 d (x, s) < r \u3068\u306a\u308b\u3088\u3046\u306a\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3068\u304d\u3001S \u306f\u6709\u754c\u3067\u3042\u308b\u3068\u3044\u3046\u3002M \u304c\u305d\u308c\u81ea\u8eab\u3092 M \u306e\u90e8\u5206\u96c6\u5408\u3068\u307f\u3066\u6709\u754c\u3067\u3042\u308b\u3068\u304d\u3001d \u3092\u6709\u754c\u8ddd\u96e2\u51fd\u6570 (bounded metric) \u3068\u3044\u3044\u3001M \u3092\u6709\u754c\u8ddd\u96e2\u7a7a\u9593 (bounded metric space) \u3068\u547c\u3076\u3002 \u3053\u3053\u3067S\u304c\u7a7a\u96c6\u5408\u3067\u306a\u3044\u3068\u304d\u306f\u4e2d\u5fc3x\u3092S\u306e\u5143\u306b\u9078\u3076\u3068\u3057\u3066\u3082\u540c\u5024\u3067\u3042\u308b\u3002\u307e\u305f\u540c\u5024\u306a\u7279\u5fb4\u4ed8\u3068\u3057\u3066S\u306e\u76f4\u5f84 diam S\u00a0:= sup{d(x, y) | x, y \u2208 S} \u304c\u6709\u9650\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308b\u3002\u4f8b\u3068\u6027\u8cea[\u7de8\u96c6]\u5b9f\u6570\u304b\u3089\u306a\u308b\u958b\u533a\u9593 (a, b) \u3084\u9589\u533a\u9593 [a, b] \u306f\uff08\u901a\u5e38\u306e\u5b9f\u6570\u306e\u5927\u5c0f\u95a2\u4fc2\u306b\u95a2\u3059\u308b\uff09\u9806\u5e8f\u96c6\u5408\u3068\u3057\u3066\u3082\uff08\u901a\u5e38\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u306b\u95a2\u3059\u308b\uff09\u8ddd\u96e2\u7a7a\u9593\u3068\u3057\u3066\u3082\u6709\u754c\u3067\u3042\u308b\u3002\u5b9f\u6570\u304b\u3089\u306a\u308b\u96c6\u5408\uff08\u5b9f\u6570\u5168\u4f53\u306e\u6210\u3059\u96c6\u5408 R \u306e\u90e8\u5206\u96c6\u5408\uff09\u304c\u6709\u754c\u306a\u3089\u3070\u3001\u305d\u308c\u3092\u542b\u3080\u6709\u754c\u533a\u9593\u304c\u5b58\u5728\u3059\u308b\u3002\u4e00\u822c\u306b\u3001Rn \u306b\u5927\u5c0f\u95a2\u4fc2\u306e\u76f4\u7a4d\u9806\u5e8f\u3068\u901a\u5e38\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3092\u5165\u308c\u3066\u8003\u3048\u308b\u3068\u304d\u3001Rn \u306e\u90e8\u5206\u96c6\u5408 S \u304c\u3053\u306e\u9806\u5e8f\u306b\u95a2\u3057\u3066\u6709\u754c\u3068\u306a\u308b\u3053\u3068\u3068\u3053\u306e\u8ddd\u96e2\u306b\u95a2\u3057\u3066\u6709\u754c\u3068\u306a\u308b\u3053\u3068\u3068\u306f\u7b49\u4fa1\u3067\u3042\u308b\u3002\u5b9f\u6570\u5168\u4f53 R \u306f\u6709\u754c\u3067\u306f\u306a\u3044\uff08\u30a2\u30eb\u30ad\u30e1\u30c7\u30b9\u6027\uff09\u3002R \u306e\u7a7a\u3067\u306a\u3044\u6709\u754c\u96c6\u5408\u306f\u4e0a\u9650\uff08\u6700\u5c0f\u4e0a\u754c\uff09\u3068\u4e0b\u9650\uff08\u6700\u5927\u4e0b\u754c\uff09\u3092\u6301\u3064\u3002\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 Rn \u306e\u6709\u754c\u96c6\u5408\u306f\u5168\u6709\u754c\u3067\u3042\u308b\u3002\u3068\u304f\u306bRn 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