# Isomorphism

[ahy-suh-mawr-fiz-uh m] /ˌaɪ səˈmɔr fɪz əm/

**noun**

1.

the state or property of being or .

2.

Mathematics. a one-to-one relation onto the map between two sets, which preserves the relations existing between elements in its domain.

/ˌaɪsəʊˈmɔːfɪzəm/

**noun**

1.

(biology) similarity of form, as in different generations of the same life cycle

2.

(chem) the existence of two or more substances of different composition in a similar crystalline form

3.

(maths) a one-to-one correspondence between the elements of two or more sets, such as those of Arabic and Roman numerals, and between the sums or products of the elements of one of these sets and those of the equivalent elements of the other set or sets

n.

from German Isomorphismus, 1828, coined by German chemist Eilhard Mitscherlich (1794-1863) from isomorph; see isomorphic. Related: Isomorph.

isomorphism i·so·mor·phism (ī’sə-môr’fĭz’əm)

n.

i’so·mor’phous **adj.**

isomorphism

(ī’sə-môr’fĭz’əm)

mathematics

A bijective map between two objects which preserves, in both directions, any structure under consideration. Thus a `group isomorphism’ preserves group structure; an order isomorphism (between posets) preserves the order relation, and so on. Usually it is clear from context what sort of isomorphism is intended.

(1995-03-25)

Tagged: i

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- Isomorphism class
mathematics A collection of all the objects isomorphic to a given object. Talking about the isomorphism class (of a poset, say) ensures that we will only consider its properties as a poset, and will not consider other incidental properties it happens to have. (1995-03-25)

- Isomorphous
[ahy-suh-mawr-fuh s] /ˌaɪ səˈmɔr fəs/ adjective, Chemistry, Crystallography. 1. (of a compound or mineral) capable of crystallizing in a form similar to that of another compound or mineral, used especially of substances so closely related that they form end members of a series of solid solutions.

- Isoneph
[ahy-suh-nef] /ˈaɪ səˌnɛf/ noun, Meteorology. 1. a line on a weather map or chart connecting points having the same amount of cloudiness.

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