homomorphismn.

/hɒməʊˈmɔːfɪz(ə)m/

Etymology: < homo- comb. form + -morphism comb. form.

1. The condition of being homomorphic; resemblance of form, esp. without real structural affinity.

ΘΚΠ

the world > life > biology > physical aspects or shapes > shape > [noun] > condition of being similar

homomorphism1869

homomorphy1874

1869 H. A. Nicholson Man. Zool. 233 Homomorphism subsists between the Polyzoa and the Hydroida.

1872 H. A. Nicholson Introd. Study Biol. 50–1 Many examples are known, both in the animal and the vegetable kingdom, in which families widely removed from one another in their fundamental structure, nevertheless present a..close resemblance. For this phenomenon the term ‘homomorphism’ has been proposed, and such forms are said to be ‘homomorphic’.

2. Mathematics. [See -morphism comb. form] 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.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements

inclusion1870

orthomorphosis1885

isomorphism1892

identity1910

homoeomorphism1918

homomorphism1935

topological mapping or transformation1939

isometry1941

Möbius transformation1941

injection map(ping)1950

monomorphism1954

bijection1963

surjection1964

1935 Duke Math. Jrnl. 1 2 There exists an operation F defined topologically for all the chains and such that F {c_p} is a homomorphism of {c_p} into {c_p–1}, and of {c₀} into the identity.

1941 G. Birkhoff & S. 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.

1959 E. M. Patterson Topol. (ed. 2) iv. 82 In fact, there is a homomorphism between the groups (not to be confused with homeomorphism).

1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. 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 ∈ R₁.

1969 F. 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′.

in extended use.1966 S. 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.

Derivatives

ˈhomoˌmorphy n.

ΘΚΠ

the world > life > biology > physical aspects or shapes > shape > [noun] > condition of being similar

homomorphism1869

homomorphy1874

1874 R. Brown Man. Bot. Gloss. Homomorphy.

1883 P. Geddes in Encycl. Brit. XVI. 845/1 Haeckel proposed to term homophyly the truly phylogenetic homology in opposition to homomorphy, to which genealogic basis is wanting.

This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2020).

单词	homomorphism
释义	homomorphismn. /hɒməʊˈmɔːfɪz(ə)m/ Etymology: < homo- comb. form + -morphism comb. form. 1. The condition of being homomorphic; resemblance of form, esp. without real structural affinity. ΘΚΠ the world > life > biology > physical aspects or shapes > shape > [noun] > condition of being similar homomorphism1869 homomorphy1874 1869 H. A. Nicholson Man. Zool. 233 Homomorphism subsists between the Polyzoa and the Hydroida. 1872 H. A. Nicholson Introd. Study Biol. 50–1 Many examples are known, both in the animal and the vegetable kingdom, in which families widely removed from one another in their fundamental structure, nevertheless present a..close resemblance. For this phenomenon the term ‘homomorphism’ has been proposed, and such forms are said to be ‘homomorphic’. 2. Mathematics. [See -morphism comb. form] 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. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements inclusion1870 orthomorphosis1885 isomorphism1892 identity1910 homoeomorphism1918 homomorphism1935 topological mapping or transformation1939 isometry1941 Möbius transformation1941 injection map(ping)1950 monomorphism1954 bijection1963 surjection1964 1935 Duke Math. Jrnl. 1 2 There exists an operation F defined topologically for all the chains and such that F {c_p} is a homomorphism of {c_p} into {c_p–1}, and of {c₀} into the identity. 1941 G. Birkhoff & S. 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. 1959 E. M. Patterson Topol. (ed. 2) iv. 82 In fact, there is a homomorphism between the groups (not to be confused with homeomorphism). 1965 E. M. Patterson & D. E. Rutherford Elem. Abstr. 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 ∈ R₁. 1969 F. 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′. in extended use.1966 S. 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. Derivatives ˈhomoˌmorphy n. ΘΚΠ the world > life > biology > physical aspects or shapes > shape > [noun] > condition of being similar homomorphism1869 homomorphy1874 1874 R. Brown Man. Bot. Gloss. Homomorphy. 1883 P. Geddes in Encycl. Brit. XVI. 845/1 Haeckel proposed to term homophyly the truly phylogenetic homology in opposition to homomorphy, to which genealogic basis is wanting. This entry has not yet been fully updated (first published 1976; most recently modified version published online June 2020). < n.1869
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