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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 Incidence structure ： ウィキペディア英語版 Incidence structure In mathematics, an abstract system consisting of two types of objects and a single relationship between these types of objects is called an incidence structure. Consider the points and lines of the Euclidean plane as the two types of objects and ignore all the properties of this geometry except for the relation of which points are on which lines for all points and lines. What is left is the incidence structure of the Euclidean plane. Incidence structures are most often considered in the geometrical context where they are abstracted from, and hence generalize, planes (such as affine, projective, and Möbius planes), but the concept is very broad and not limited to geometric settings. Even in a geometric setting, incidence structures are not limited to just points and lines; higher-dimensional objects (planes, solids, -spaces, conics, etc.) can be used. The study of finite structures is sometimes called finite geometry. ==Formal definition and terminology== An incidence structure is a triple () where is a set whose elements are called ''points'', is a disjoint set whose elements are called ''lines'' and is the incidence relation. The elements of are called flags. If () is in then it was typical to say that point "lies on" line or that the line "passes through" point . However, today a more "symmetric" terminology is preferred to reflect the symmetric nature of this relation, so one says that " is ''incident'' with " or that " is incident with " and uses the notation in lieu of . In some common situations may be a set of subsets of in which case incidence will be containment ( if and only if is a member of ). Incidence structures of this type are called ''set-theoretic''. This is not always the case, for example, if is a set of vectors and a set of square matrices, we may define vector is an eigenvector of matrix }. This example also shows that while the geometric language of points and lines is used, the object types need not be these geometric objects. 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「Incidence structure」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.