翻訳と辞書 Words near each other ・ Inclusion (education) ・ Inclusion (logic) ・ Inclusion (mineral) ・ Inclusion (taxonomy) ・ Inclusion (value and practice) ・ Inclusion and Democracy ・ Inclusion and exclusion criteria ・ Inclusion bodies ・ Inclusion Body Disease ・ Inclusion body myositis ・ Inclusion body rhinitis ・ Inclusion compound ・ Inclusion Films ・ Inclusion Healthcare ・ Inclusion Hill ・ Inclusion map ・ Inclusion Melbourne ・ Inclusion probability ・ Inclusionary zoning ・ Inclusionism ・ Inclusion–exclusion principle ・ Inclusive ・ Inclusive business ・ Inclusive business finance ・ Inclusive business model ・ Inclusive capitalism ・ Inclusive Church ・ Inclusive composite interval mapping ・ Inclusive Democracy ・ Inclusive Design Research Centre 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 Inclusion map ： ウィキペディア英語版 Inclusion map In mathematics, if $A$ is a subset of $B$, then the inclusion map (also inclusion function, insertion, or canonical injection) 〔, page 5〕 is the function $\backslash iota$ that sends each element, $x$ of $A$ to $x$, treated as an element of $B$: :$\backslash iota:\; A\backslash rightarrow\; B,\; \backslash qquad\; \backslash iota(x)=x.$ A "hooked arrow" $\backslash hookrightarrow$ is sometimes used in place of the function arrow above to denote an inclusion map. This and other analogous injective functions 〔, page 1 〕 from substructures are sometimes called ''natural injections''. Given any morphism ''f'' between objects ''X'' and ''Y'', if there is an inclusion map into the domain $\backslash iota\; :\; A\backslash rightarrow\; X$, then one can form the restriction ''fi'' of ''f''. In many instances, one can also construct a canonical inclusion into the codomain ''R''→''Y'' known as the range of ''f''. == Applications of inclusion maps == Inclusion maps tend to be homomorphisms of algebraic structures; thus, such inclusion maps are embeddings. More precisely, given a sub-structure closed under some operations, the inclusion map will be an embedding for tautological reasons. For example, for a binary operation $\backslash star$, to require that :$\backslash iota(x\backslash star\; y)=\backslash iota(x)\backslash star\; \backslash iota(y)$ is simply to say that $\backslash star$ is consistently computed in the sub-structure and the large structure. The case of a unary operation is similar; but one should also look at nullary operations, which pick out a ''constant'' element. Here the point is that closure means such constants must already be given in the substructure. Inclusion maps are seen in algebraic topology where if ''A'' is a strong deformation retract of ''X'', the inclusion map yields an isomorphism between all homotopy groups (i.e. is a homotopy equivalence) Inclusion maps in geometry come in different kinds: for example embeddings of submanifolds. Contravariant objects such as differential forms ''restrict'' to submanifolds, giving a mapping in the ''other direction''. Another example, more sophisticated, is that of affine schemes, for which the inclusions :''Spec(R/I)'' → ''Spec(R)'' and :''Spec(R/I2)'' → ''Spec(R)'' may be different morphisms, where ''R'' is a commutative ring and ''I'' an ideal. 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「Inclusion map」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.