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# ALL meanings of isomorphism

i·so·mor·phism
I i
• noun Technical meaning of isomorphism (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. 1
• noun isomorphism Similarity of form. 1
• noun isomorphism the state or property of being isomorphous or isomorphic. 1
• noun isomorphism Mathematics. a one-to-one relation onto the map between two sets, which preserves the relations existing between elements in its domain. 1
• noun isomorphism similarity of form, as in different generations of the same life cycle 0
• noun isomorphism the existence of two or more substances of different composition in a similar crystalline form 0
• noun isomorphism 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 0
• noun isomorphism a similarity in appearance or structure of organisms belonging to different species or races 0
• noun isomorphism an identity or close similarity in the crystalline form of substances usually containing different elements but having similar composition 0
• noun isomorphism a one-to-one correspondence between two mathematical systems, sets, etc. that preserves the basic operations, as the correspondence between binary numbers and decimal numbers, each a set of real numbers 0