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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Simplicial complex ： ウィキペディア英語版 Simplicial complex In mathematics, a simplicial complex is a topological space of a certain kind, constructed by "gluing together" points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration). Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. ==Definitions== A simplicial complex $\backslash mathcal$ is a set of simplices that satisfies the following conditions: :1. Any face of a simplex from $\backslash mathcal$ is also in $\backslash mathcal$. :2. The intersection of any two simplices $\backslash sigma\_1,\; \backslash sigma\_2\; \backslash in\; \backslash mathcal$ is either $\backslash emptyset$ or a face of both $\backslash sigma\_1$ and $\backslash sigma\_2$. Note that the empty set is a face of every simplex. See also the definition of an abstract simplicial complex, which loosely speaking is a simplicial complex without an associated geometry. A simplicial ''k''-complex $\backslash mathcal$ is a simplicial complex where the largest dimension of any simplex in $\backslash mathcal$ equals ''k''. For instance, a simplicial 2-complex must contain at least one triangle, and must not contain any tetrahedra or higher-dimensional simplices. A pure or homogeneous simplicial ''k''-complex $\backslash mathcal$ is a simplicial complex where every simplex of dimension less than ''k'' is a face of some simplex $\backslash sigma\; \backslash in\; \backslash mathcal$ of dimension exactly ''k''. Informally, a pure 1-complex "looks" like it's made of a bunch of lines, a 2-complex "looks" like it's made of a bunch of triangles, etc. An example of a ''non''-homogeneous complex is a triangle with a line segment attached to one of its vertices. A facet is any simplex in a complex that is ''not'' a face of any larger simplex. (Note the difference from a "face" of a simplex). A pure simplicial complex can be thought of as a complex where all facets have the same dimension. Sometimes the term ''face'' is used to refer to a simplex of a complex, not to be confused with a face of a simplex. For a simplicial complex embedded in a ''k''-dimensional space, the ''k''-faces are sometimes referred to as its cells. The term ''cell'' is sometimes used in a broader sense to denote a set homeomorphic to a simplex, leading to the definition of cell complex. The underlying space, sometimes called the carrier of a simplicial complex is the union of its simplices. 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「Simplicial complex」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.