| 释义 |
homomorphism|hɒməʊˈmɔːfɪz(ə)m|
[f. homo- + Gr. µορϕ-ή form + -ism.]
1. The condition of being homomorphic; resemblance of form, esp. without real structural affinity; also ˈhomoˌmorphy.
1869Nicholson Zool. 233 Homomorphism subsists between the Polyzoa and the Hydroida. 1872[see homomorphic a. 1 a.] 1874R. Brown Man. Bot. Gloss., Homomorphy. 1883Homomorphy [see homophyly s.v. homo-].
2. Math. [See ] A many-to-one (or one-to-one) transformation of one set into another that preserves in the second set the operations or relations between the elements of the first.
1935Duke Math. Jrnl. I. 2 There exists an operation F defined topologically for all the chains and such that F {ob}cp{cb} is a homomorphism of {ob}cp{cb} into {ob}cp–1{cb}, and of {ob}c0{cb} into the identity. 1941Birkhoff & MacLane Surv. Mod. Algebra vi. 155 Under any homomorphism G→ G′, the identity e of G goes into the identity of G′, and inverses into inverses. 1959E. M. Patterson Topology (ed. 2) iv. 82 In fact, there is a homomorphism between the groups (not to be confused with homeomorphism). 1965Patterson & Rutherford Elem. Abstract Algebra iii. 79 A mapping f of a ring R1 into a ring R2 is called a homomorphism if f(x + y) = f(x) + f(y), f(xy) = f(x)f(y) for all x, y {elem} R1. 1969F. Harary Graph Theory xii. 143 If G′ is the graph resulting from a homomorphism ϕ of G we can consider ϕ as a function from V onto V′ such that if u and v are adjacent in G, then ϕu and ϕv are adjacent in G′.
transf.1966S. Beer Decision & Control vi. 113 A scientific model is a homomorphism on to which two different situations are mapped, and which actually defines the extent to which they are structurally identical. |