different between isomorphic vs isotrivial

English

Etymology

From iso- +? -morphic.

Pronunciation

• (UK) enPR: ?s?mô'f?k, IPA^(key): /?a?.s??m??.f?k/
• (US) enPR: ?s?môr'f?k, IPA^(key): /?a?.so??m??.f?k/
• Rhymes: -??(r)f?k

Adjective

isomorphic (not comparable)

1. (mathematics) Related by an isomorphism; having a structure-preserving one-to-one correspondence.
   • 2003, Bernd Siegfried Walter Schröder, page 254

     Let A, B be the ordered sets in Figure 10.3. Let C be the direct product of infinitely many copies of the two element chain 2. Then A^C is isomorphic to B^C, but A is not isomorphic to B.

2. (biology) Having a similar structure or function to something that is not related genetically or through evolution.
   • 1993, Marcus Jacobson, Foundations of Neuroscience, page 106

     The fact that different structures can be shown to be functionally isomorphic implies that they are analogous, not homologous.

3. Having identical relevant structure; being structure-preserving while undergoing certain invertible transformations.
   • 1981, John Lyons, Language and Linguistics: An Introduction, page 60

     For example, in so far as written and spoken English are isomorphic (i.e. have the same structure), they are the same language: there is nothing but their structure that they have in common.

Usage notes

• In mathematics, this adjective can be used in phrases like "A and B are isomorphic", "A is isomorphic to B", and, less commonly, "A is isomorphic with B".

Antonyms

• anisomorphic
• nonisomorphic

Coordinate terms

• anisomorphic
• heteromorphic
• homomorphic

Derived terms

• anisomorphic
• isomorphically

Related terms

• isomorph
• isomorphism
• isomorphous

Translations

Further reading

• isomorphic keyboard on Wikipedia.Wikipedia

English

Etymology

iso- +? trivial

Adjective

isotrivial (not comparable)

1. (mathematics) Describing a smooth projective surface having a morphism onto a curve such that all smooth fibres are isomorphic to each other

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