翻訳と辞書 Words near each other ・ Solid state ionics ・ Solid State Ionics (journal) ・ Solid State Logic ・ Solid State Pharmaceutical Cluster ・ Solid State Phased Array Radar System ・ Solid State Physics Laboratory ・ Solid State Records ・ Solid State Records (jazz label) ・ Solid State Rhyme ・ Solid State Survivor ・ Solid State Warrior ・ Solid Steel ・ Solid stress ・ Solid surface ・ Solid sweep ・ Solid torus ・ Solid trigonometry ・ Solid unbleached board ・ Solid Waste Agency of Northern Cook County v. Army Corps of Engineers ・ Solid Waste Association of North America ・ Solid Waste Disposal Act of 1965 ・ Solid waste policy in India ・ Solid waste policy in the United States ・ Solid white (chicken plumage) ・ Solid wood ・ Solid Wood (song) ・ Solid-fuel rocket ・ Solid-phase microextraction ・ Solid-phase synthesis ・ Solid-state battery Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Solid torus ： ウィキペディア英語版 Solid torus In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle.〔.〕 It is homeomorphic to the Cartesian product $S^1\; \backslash times\; D^2$ of the disk and the circle,〔.〕 endowed with the product topology. A standard way to visualize a solid torus is as a toroid, embedded in 3-space. However, it should be distinguished from a torus, which has the same visual appearance: the torus is the two-dimensional space on the boundary of a toroid, while the solid torus includes also the interior space surrounded by the torus. ==Topological properties== The solid torus is a connected, compact, orientable 3-dimensional manifold with boundary. The boundary is homeomorphic to $S^1\; \backslash times\; S^1$, the ordinary torus. Since the disk $D^2$ is contractible, the solid torus has the homotopy type of a circle, $S^1$.〔.〕 Therefore the fundamental group and homology groups are isomorphic to those of the circle: :$\backslash pi\_1(S^1\; \backslash times\; D^2)\; \backslash cong\; \backslash pi\_1(S^1)\; \backslash cong\; \backslash mathbb,$ :$H\_k(S^1\; \backslash times\; D^2)\; \backslash cong\; H\_k(S^1)\; \backslash cong$ \begin \mathbb & \mbox k = 0,1 \\ 0 & \mbox \end. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Solid torus」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.