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Isomorphism vs Homogeneous - What's the difference?

isomorphism | homogeneous |

As a noun isomorphism

is similarity of form.

As an adjective homogeneous is

of the same kind; alike, similar.

isomorphism

English

Noun

(en noun)
  • Similarity of form
  • * 1984 Brigitte Asbach-Schnitker, "Introduction", Mercury or The Secret and Swift Messenger , ISBN 9027232768.
    • The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages.
    :
  • (biology) the similarity in form of organisms of different ancestry
    • :
  • (chemistry) the similarity in the crystal structures of similar chemical compounds
    • :
  • * 1874 C. Rammelsberg, "Crystallographic and chemical relations of the natural sulphides, arsenides, and sulpharsenides", The Chemical News and Journal of Physical Science , page 197.
    • :
    The isomorphism' of compounds does not prove the ' isomorphism of their respective constituents.
    :
  • (sociology) the similarity in the structure or processes of different organizations
    • :  2.  A one-to-one correspondence :
  • (group algebra) A bijection f'' such that both ''f'' and its inverse ''f  −1 are homomorphisms, that is, structure-preserving mappings.
    • :
  • (computer science) 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
    • :
  • (category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).

    • Abbreviations

    * (in category theory) iso

    Related terms

    * isomorphic * isomorphous

    See also

    * ("isomorphism" on Wikipedia)

    homogeneous

    English

    Alternative forms

    * (proscribed)

    Adjective

    (-)
  • Of the same kind; alike, similar.
  • Having the same composition throughout; of uniform make-up.
  • * 1946 , (Bertrand Russell), History of Western Philosophy , I.25:
    • Their citizens were not of homogeneous origin, but were from all parts of Greece.
  • (chemistry) in the same state of matter.
  • (mathematics) Of which the properties of a smaller set apply to the whole; scalable.
    • The function ''f(x,y)=x2+y2'' is homogeneous of degree 2 because ''f(''?''x,''?''y)=''?''2f(x,y)''.
  • (proscribed)

    • Antonyms

    * heterogeneous

    Related terms

    * homogeneity * homogenise, homogenize

    Derived terms

    * homogeneous mixture * homogeneous broadening * homogeneous catalysis * homogeneous coordinate * homogeneous function * homogeneous ideal * homogeneous number * homogeneous polynomial * homogeneous radiation * homogeneous society * homogeneous space * homogeneous system

    External links

    * * * English words prefixed with homo-