From haskell-jp=return@quickml.com Fri Jul 1 15:17:54 2005 Received: from kankan.nagaokaut.ac.jp (kankan.nagaokaut.ac.jp [133.44.2.24]) by blade.nagaokaut.ac.jp (8.12.3/8.12.3/Debian-6.6) with ESMTP id j616HrgZ030747; Fri, 1 Jul 2005 15:17:54 +0900 Received: from funfun.nagaokaut.ac.jp (funfun.nagaokaut.ac.jp [133.44.2.201]) by kankan.nagaokaut.ac.jp (Postfix) with ESMTP id 4808658D2; Fri, 1 Jul 2005 15:17:54 +0900 (JST) Received: from localhost (localhost.nagaokaut.ac.jp [127.0.0.1]) by funfun.nagaokaut.ac.jp (Postfix) with ESMTP id 75D8DF0487B; Fri, 1 Jul 2005 15:17:56 +0900 (JST) Received: from voscc.nagaokaut.ac.jp (voscc.nagaokaut.ac.jp [133.44.1.100]) by funfun.nagaokaut.ac.jp (Postfix) with ESMTP id 3471EF0484A; Fri, 1 Jul 2005 15:17:55 +0900 (JST) Received: from master.quickml.com (219-106-226-205.cust.bit-drive.ne.jp [219.106.226.205]) by voscc.nagaokaut.ac.jp (Postfix) with ESMTP id 23C25630071; Fri, 1 Jul 2005 15:17:54 +0900 (JST) Received: from master.quickml.com (localhost [127.0.0.1]) by master.quickml.com (Postfix) with ESMTP id 054601F317F; Fri, 1 Jul 2005 15:17:52 +0900 (JST) Received: from master.quickml.com (localhost [127.0.0.1]) by localhost (QuickML) with ESMTP; Fri, 01 Jul 2005 15:17:51 +0900 Received: from ranran.nagaokaut.ac.jp (ranran.nagaokaut.ac.jp [133.44.2.25]) by master.quickml.com (Postfix) with ESMTP id 70A591F317F for ; Fri, 1 Jul 2005 15:17:51 +0900 (JST) Received: from sav2.nagaokaut.ac.jp (sav2.nagaokaut.ac.jp [133.44.2.23]) by ranran.nagaokaut.ac.jp (Postfix) with ESMTP id 401164669BE for ; Fri, 1 Jul 2005 15:17:49 +0900 (JST) Received: from localhost (localhost.nagaokaut.ac.jp [127.0.0.1]) by sav2.nagaokaut.ac.jp (Postfix) with ESMTP id 63001462095 for ; Fri, 1 Jul 2005 15:17:51 +0900 (JST) Received: from smtp.nagaokaut.ac.jp (smtp2.nagaokaut.ac.jp [133.44.2.38]) by sav2.nagaokaut.ac.jp (Postfix) with ESMTP id A2AA5462092 for ; Fri, 1 Jul 2005 15:17:49 +0900 (JST) Received: from blade.nagaokaut.ac.jp (blade.nagaokaut.ac.jp [133.44.98.95]) by smtp.nagaokaut.ac.jp (Postfix) with SMTP id D16435221 for ; Fri, 1 Jul 2005 15:17:49 +0900 (JST) Received: from BOOK.blade.nagaokaut.ac.jp (sinara@blade.nagaokaut.ac.jp [133.44.98.95]) by blade.nagaokaut.ac.jp (8.12.3/8.12.3/Debian-6.6) with ESMTP id j616Hkga030721 for ; Fri, 1 Jul 2005 15:17:46 +0900 Message-Id: <6.1.0.6.2.20050701150519.02c59808@localhost> X-Sender: sinara@localhost (Unverified) X-Mailer: QUALCOMM Windows Eudora Version 6J Jr6-rev2 Date: Fri, 01 Jul 2005 15:17:19 +0900 To: haskell-jp@quickml.com From: Shin-ichiro HARA In-Reply-To: <42C23A4B.4020807@mac.com> References: <42C23A4B.4020807@mac.com> Mime-Version: 1.0 Content-Type: text/plain; charset="ISO-2022-JP" Content-Transfer-Encoding: 7bit X-Virus-Scanned: by AMaViS snapshot-20020531 Subject: [haskell-jp:682] Re: =?iso-2022-jp?B?GyRCTyJCM0AtJEhJVEYwRUAkTjRYNzgbKEI=?= =?iso-2022-jp?B?ICA=?= Reply-To: haskell-jp@quickml.com Reply-To: haskell-jp@quickml.com X-Mail-Count: 682 Precedence: bulk X-ML-Address: haskell-jp@quickml.com X-ML-Name: haskell-jp X-ML-Info: http://QuickML.com/ X-QuickML: true X-Virus-Scanned: by AMaViS snapshot-20020531 原です。 >野中でございます。 > >どうも独り言みたいなものですみませんが... > >閉区間I=[0,1] > >f:I->Iとしたとき > >fが不動点を持つということは、xy平面上のグラフで考えると、y=xという斜め45 >度のグラフとfが交わるということなのですね。 つけ加えると、これの２次元バージョン f:I^2 -> I^2 においても４次元立方体に２次元の対角「面」があって、fの不動点は fの作る曲面と対角面との交点と考えられるわけです。 「fが連続なら必ずこの対角面との交点が存在する」というのが不動点 定理ですが、その証明は１次元の場合に比べなぜか突然難しくなって、 何らかの幾何学的手法が必要なはずです。"Coceptiual Mathematics" ではそのあたりどう処理してるんでしょう？ ちなみに優秀な幾何学者はこの対角面が「見える」そうです。私には全 く見えません。(^^;) -- ML: haskell-jp@quickml.com 使い方: http://QuickML.com/