翻訳と辞書 Words near each other ・ Transylvania, Louisiana ・ Transylvanian Diet ・ Transylvanian Hound ・ Transylvanian Landler ・ Transylvanian Memorandum ・ Transversal ・ Transversal (combinatorics) ・ Transversal (geometry) ・ Transversal (instrument making) ・ Transversal 86 (TransMilenio) ・ Transversal Corporation ・ Transversal plane ・ Transversal programme ・ Transversal Theater Company ・ Transversality ・ Transversality (mathematics) ・ Transversality theorem ・ Transverse ・ Transverse abdominal muscle ・ Transverse acetabular ligament ・ Transverse aeolian ridges ・ Transverse arrowhead ・ Transverse artery ・ Transverse axis ・ Transverse boiler ・ Transverse branch of lateral circumflex femoral artery ・ Transverse cervical artery ・ Transverse cervical nerve ・ Transverse cervical veins ・ Transverse City 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 Transversality (mathematics) ： ウィキペディア英語版 Transversality (mathematics) In mathematics, transversality is a notion that describes how spaces can intersect; transversality can be seen as the "opposite" of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is defined by considering the linearizations of the intersecting spaces at the points of intersection. ==Definition== Two submanifolds of a given finite-dimensional smooth manifold are said to intersect transversally if at every point of intersection, their separate tangent spaces at that point together generate the tangent space of the ambient manifold at that point.〔Guillemin and Pollack 1974, p.30.〕 Manifolds that do not intersect are vacuously transverse. If the manifolds are of complementary dimension (i.e., their dimensions add up to the dimension of the ambient space), the condition means that the tangent space to the ambient manifold is the direct sum of the two smaller tangent spaces. If an intersection is transverse, then the intersection will be a submanifold whose codimension is equal to the sums of the codimensions of the two manifolds. In the absence of the transversality condition the intersection may fail to be a submanifold, having some sort of singular point. In particular, this means that transverse submanifolds of complementary dimension intersect in isolated points (i.e., a 0-manifold). If both submanifolds and the ambient manifold are oriented, their intersection is oriented. When the intersection is zero-dimensional, the orientation is simply a plus or minus for each point. One notation for the transverse intersection of two submanifolds ''L''1 and ''L''2 of a given manifold ''M'' is $L\_\; \backslash pitchfork\; L\_$. This notation can be read in two ways: either as “''L''1 and ''L''2 intersect transversally” or as an alternative notation for the set-theoretic intersection ''L''1 ∩ ''L''2 of ''L''1 and ''L''2 when that intersection is transverse. In this notation, the definition of transversality reads :$L\_\; \backslash pitchfork\; L\_\; \backslash iff\; \backslash forall\; p\; \backslash in\; L\_\; \backslash cap\; L\_,\; \backslash mathrm\_\; M\; =\; \backslash mathrm\_\; L\_\; +\; \backslash mathrm\_\; L\_.$ 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「Transversality (mathematics)」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.