[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2461#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2461","headline":"\u30d5\u30a9\u30ed\u30fc-Up Compactness -Wikipedia","name":"\u30d5\u30a9\u30ed\u30fc-Up Compactness -Wikipedia","description":"before-content-x4 \u6570\u5b66\u306b\u306f\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u9818\u57df\u304c\u3042\u308a\u307e\u3059 -up compact\u3092\u30d5\u30a9\u30ed\u30fc\u3057\u307e\u3059 \u5404\u30a8\u30d4\u30bd\u30fc\u30c9\u306b\u53ce\u675f\u90e8\u5206\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u3042\u308b\u5834\u5408\u3002\u30e1\u30c8\u30ea\u30c3\u30af\u30eb\u30fc\u30e0\u306f\u3001\u5b8c\u5168\u306b\u5236\u9650\u3055\u308c\u305f\u5b8c\u5168\u306a\u3001\u3064\u307e\u308a\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u5834\u5408\u3001\u307e\u3055\u306b\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u306e\u90e8\u5206\u91cf r n {displaystyle mathbb {r} ^{n}} after-content-x4 \u3053\u308c\u306f\u3001\u9589\u3058\u3089\u308c\u3066\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u3068\u304d\u306b\u3001\u307e\u3055\u306b\u305d\u308c\u306b\u7d9a\u304f\uff08\u305d\u3057\u3066\u30b3\u30f3\u30d1\u30af\u30c8\u306a\uff09\u3082\u306e\u3067\u3059\u3002\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u3044\u30c8\u30dd\u30ed\u30b8\u30fc\u30eb\u30fc\u30e0\u304c\u3042\u308a\u3001\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u304f\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30b9\u30da\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002 Table of Contents \u30c8\u30dd\u30ed\u30b8\u30fc\u30eb\u30fc\u30e0\u306e\u53ce\u675f\u7684\u306a\u7d50\u679c [ \u7de8\u96c6 |","datePublished":"2022-05-22","dateModified":"2022-05-22","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/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\/c510b63578322050121fe966f2e5770bea43308d","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c510b63578322050121fe966f2e5770bea43308d","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2461","wordCount":6777,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u6570\u5b66\u306b\u306f\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u9818\u57df\u304c\u3042\u308a\u307e\u3059 -up compact\u3092\u30d5\u30a9\u30ed\u30fc\u3057\u307e\u3059 \u5404\u30a8\u30d4\u30bd\u30fc\u30c9\u306b\u53ce\u675f\u90e8\u5206\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u3042\u308b\u5834\u5408\u3002\u30e1\u30c8\u30ea\u30c3\u30af\u30eb\u30fc\u30e0\u306f\u3001\u5b8c\u5168\u306b\u5236\u9650\u3055\u308c\u305f\u5b8c\u5168\u306a\u3001\u3064\u307e\u308a\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u5834\u5408\u3001\u307e\u3055\u306b\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u306e\u90e8\u5206\u91cf r n {displaystyle mathbb {r} ^{n}}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3053\u308c\u306f\u3001\u9589\u3058\u3089\u308c\u3066\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u3068\u304d\u306b\u3001\u307e\u3055\u306b\u305d\u308c\u306b\u7d9a\u304f\uff08\u305d\u3057\u3066\u30b3\u30f3\u30d1\u30af\u30c8\u306a\uff09\u3082\u306e\u3067\u3059\u3002\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u3044\u30c8\u30dd\u30ed\u30b8\u30fc\u30eb\u30fc\u30e0\u304c\u3042\u308a\u3001\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u304f\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30b9\u30da\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002 Table of Contents\u30c8\u30dd\u30ed\u30b8\u30fc\u30eb\u30fc\u30e0\u306e\u53ce\u675f\u7684\u306a\u7d50\u679c [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d5\u30a1\u30ed\u30fc\u30a2\u30c3\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u3044\u30b3\u30f3\u30d1\u30af\u30c8\u30cf\u30a6\u30b9\u30c9\u30fc\u30d5\u30eb\u30fc\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30b3\u30f3\u30d1\u30af\u30c8\u3067\u306f\u306a\u3044\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b9\u30da\u30fc\u30b9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30c8\u30dd\u30ed\u30b8\u30fc\u30eb\u30fc\u30e0\u306e\u53ce\u675f\u7684\u306a\u7d50\u679c [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u306f        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\uff08 \u30d0\u30c4 \u3001 d \uff09\uff09 {displaystyle\uff08x\u3001d\uff09} \u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593\u306a\u306e\u3067\u30011\u3064\u306e\u30a8\u30d4\u30bd\u30fc\u30c9\u304c\u5909\u63db\u3055\u308c\u307e\u3059 \uff08 \u30d0\u30c4 \u79c1 \uff09\uff09 \u79c1 \u2208 N{displaystyle\uff08x_ {i}\uff09_ {iin mathbb {n}}}}} \u3068 \u30d0\u30c4 \u79c1 \u2208 \u30d0\u30c4 {displaystyle x_ {i} in x} \u306b\u5bfe\u3057\u3066 \u30d0\u30c4 \u2208 \u30d0\u30c4 {displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059x} \u3001 \u3082\u3057\u3082        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u2200 \u03f5 > 0  \u2203 n \u2208 n  \u2200 \u79c1 \u2265 n \uff1a  d \uff08 \u30d0\u30c4 i\u3001 \u30d0\u30c4 \uff09\uff09 < \u03f5 {displaystyle forall epsilon> 0\u306fnin mathbb {n} forall igeq n\uff1ad\uff08x_ {i}\u3001x\uff09\u5b58\u5728\u3057\u307e\u3059 \u3002 \u3064\u307e\u308a\u3001\u30a8\u30d4\u30bd\u30fc\u30c9\u304c\u6b63\u78ba\u306b\u53cd\u5bfe\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u6b63\u306e\u5b9f\u6570\u304c\u3042\u308b\u3068\u304d\u306b\u53ce\u675f\u3057\u307e\u3059 \u03f5 {displaystyle epsilon} \u81ea\u7136\u6570 n {displaystyle n} \u4ee5\u964d\u306e\u3059\u3079\u3066\u306e\u30e1\u30f3\u30d0\u30fc\u304c\u304b\u3089\u3059\u3079\u3066\u3092\u4e0e\u3048\u307e\u3059 n {displaystyle n}  &#8211; \u8ddd\u96e2\u3092\u30e1\u30f3\u30d0\u30fc\u306b\u3057\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u3088\u308a\u5c11\u306a\u3044\u3082\u306e\u3092\u6301\u3063\u3066\u3044\u307e\u3059 \u03f5 {displaystyle epsilon} \u306f\u3002 \u30c8\u30dd\u30ed\u30b8\u30fc\u30ed\u30b8\u30ab\u30eb\u306e\u90e8\u5c4b\u3067\u306f\u3001\u30aa\u30fc\u30d7\u30f3\u03b5\u30dc\u30fc\u30eb\u306e\u4ee3\u308f\u308a\u306b\u74b0\u5883\u304c\u767a\u751f\u3057\u307e\u3059 b \u03f5 \uff08 \u30d0\u30c4 \uff09\uff09 = { \u3068 \u2208 \u30d0\u30c4 &#8216; d \uff08 \u3068 \u3001 \u30d0\u30c4 \uff09\uff09 < \u03f5 } {displaystyle b_ {epsilon}\uff08x\uff09= {yin xmid d\uff08y\u3001x\uff09 \u30d0\u30c4 {displaystyle x_ {i} in x} \u306b\u5bfe\u3057\u3066 \u30d0\u30c4 \u2208 \u30d0\u30c4 {displaystyle\u3092\u304a\u9858\u3044\u3057\u307e\u3059x} \u305d\u308c\u304c\u3059\u3079\u3066\u306e\u74b0\u5883\u306b\u3042\u308b\u5834\u5408 \u306e {displaystyleu} \u304b\u3089 \u30d0\u30c4 {displaystyle x} a n \u2208 n {displaystyle nin mathbb {n}} \u305d\u308c\u3092\u4e0e\u3048\u308b \u30d0\u30c4 \u79c1 \u2208 \u306e {displaystyle x_ {i} in u} \u3059\u3079\u3066\u306e\u4eba\u306b\u9069\u7528\u3055\u308c\u307e\u3059 \u79c1 \u2265 n {displaystyle igeq n} \u3002 \u30d5\u30a1\u30ed\u30fc\u30a2\u30c3\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u30a8\u30ea\u30a2 \u30d0\u30c4 {displaystyle x} \u5404\u30a8\u30d4\u30bd\u30fc\u30c9\u306e\u5834\u5408\u3001\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3068\u547c\u3070\u308c\u307e\u3059 \uff08 \u30d0\u30c4 \u79c1 \uff09\uff09 \u79c1 \u2208 N{displaystyle\uff08x_ {i}\uff09_ {iin mathbb {n}}}}} \u3068 \u30d0\u30c4 \u79c1 \u2208 \u30d0\u30c4 {displaystyle x_ {i} in x} \u53ce\u675f\u90e8\u5206\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30011\u3064\u306f\u90e8\u5206\u9818\u57df\u3068\u547c\u3070\u308c\u307e\u3059 k \u2282 \u30d0\u30c4 {displaystyle ksubset x} \u5404\u30a8\u30d4\u30bd\u30fc\u30c9\u306e\u5834\u5408\u306f-up\u30b3\u30f3\u30d1\u30af\u30c8\u3092\u30d5\u30a9\u30ed\u30fc\u3057\u307e\u3059 \uff08 \u30d0\u30c4 \u79c1 \uff09\uff09 \u79c1 \u2208 N{displaystyle\uff08x_ {i}\uff09_ {iin mathbb {n}}}}} \u3068 \u30d0\u30c4 \u79c1 \u2208 k {displaystyle x_ {i} in k} \u5236\u9650\u5024\u304c\u3042\u308b\u53ce\u675f\u90e8\u5206\u30b7\u30fc\u30b1\u30f3\u30b9 k {displaystyle k} \u6240\u6709\u3002 \u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593\u306f\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u5834\u5408\u3001\u307e\u3055\u306b\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002\u30e1\u30c8\u30ea\u30c3\u30af\u30b9\u30da\u30fc\u30b9\u306f\u3001\u5b8c\u5168\u306b\u5236\u9650\u3055\u308c\u305f\u5b8c\u4e86\u3067\u3042\u308c\u3070\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3042\u308b\u305f\u3081\u3067\u3059\u3002 \u30e1\u30c8\u30ea\u30c3\u30af\u30b9\u30da\u30fc\u30b9\u304c\u5b8c\u5168\u306b\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u5404\u30a8\u30d4\u30bd\u30fc\u30c9\u306b\u306f\u90e8\u5206\u7684\u306a\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066Cauchy\u30a8\u30d4\u30bd\u30fc\u30c9\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u3082\u5b8c\u5168\u3067\u3042\u308b\u5834\u5408\u3001\u3053\u306e\u7d50\u679c\u306f\u53ce\u675f\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u30e1\u30c8\u30ea\u30c3\u30af\u30b9\u30da\u30fc\u30b9\u306f\u3001\u30d5\u30a9\u30ed\u30fc\u30a2\u30c3\u30d7\u30b3\u30f3\u30d1\u30af\u30c8\u3067\u3059\u3002\u6700\u521d\u306e\u30d5\u30a1\u30c3\u30b7\u30e7\u30f3\u6027\u306e\u3042\u308b\u30b3\u30f3\u30d1\u30af\u30c8\u30b9\u30da\u30fc\u30b9\u306f\u3001\u3088\u308a\u4e00\u822c\u7684\u3067\u3059\u3002 \u7d50\u679c\u3068\u3057\u3066\u9006\u306b\u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u306f\u5b8c\u5168\u306b\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3046\u3057\u306a\u3044\u3068\u3001 "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/2461#breadcrumbitem","name":"\u30d5\u30a9\u30ed\u30fc-Up Compactness -Wikipedia"}}]}]