English Explanatory Dictionary

isomorphism

English dictionary entry

Meanings

noun

Similarity of form
the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.
the similarity in the crystal structures of similar chemical compounds.
the similarity in the structure or processes of different organizations.
A one-to-one correspondence
A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings.
a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets.
A morphism which has a two-sided inverse; the composition of the morphism and such an inverse yields either one of two identity morphisms (depending on the order of composition).

Pronunciation

/ˌaɪsə(ʊ)ˈmɔɹfɪzəm/ en-us-isomorphism.ogg

Word forms

isomorphism isomorphisms

Etymology

From iso- + -morphism.

Synonyms

iso

Antonyms

anisomorphism

Related words

isomorphic isomorphous Isomorphism on Encyclopedia of Mathematics isomorphism on nLab Isomorphism on Wolfram MathWorld Graph Isomorphism on Wolfram MathWorld Natural Isomorphism on Wolfram MathWorld

Derived words

Curry-Howard isomorphism first isomorphism theorem natural isomorphism quasi-isomorphism ring isomorphism symplectomorphism

Translations

Bulgarian: изоморфизъм Chinese Mandarin: 同構 /同构 Czech: izomorfismus Danish: isomorfi Dutch: isomorfisme Esperanto: izomorfio Finnish: isomorfismi French: isomorphisme German: Isomorphismus Hindi: तुल्याकारिता Hindi: समाकृतिकता Hungarian: izomorfia Icelandic: einsmótun Kazakh: изоморфизм Polish: izomorfizm Portuguese: isomorfismo Russian: изоморфизм Spanish: isomorfismo

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