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A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines. Each line is a distinct subset of the points. The points in a line are said to be incident with the line. Any two lines may have no more than one point in common. Intuitively, this rule can be visualized as two straight lines, which never intersect more than once. (Finite) linear spaces can be seen as a generalization of projective and affine planes, and more broadly, of 2- block designs, where the requirement that every block contains the same number of points is dropped and the essential structural characteristic is that 2 points are incident with exactly 1 line. The term ''linear space'' was coined by Libois in 1964, though many results about linear spaces are much older. ==Definition== Let ''L'' = (''P'', ''G'', ''I'') be an incidence structure, for which the elements of ''P'' are called points and the elements of ''G'' are called lines. ''L'' is a ''linear space'' if the following three axioms hold: *(L1) two points are incident with exactly one line. *(L2) every line is incident to at least two points. *(L3) ''L'' contains at least two lines. Some authors drop (L3) when defining linear spaces. In such a situation the linear spaces complying to (L3) are considered as ''nontrivial'' and those who don't as ''trivial''. 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「Linear space (geometry)」の詳細全文を読む スポンサード リンク
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