Isomorphism (disambiguation)
Encyclopedia
Etymology: iso- + -morphism
From Ancient Greek: (isos, “equal”)
-morphism: the state of having a specified shape or form
Isomorphism may refer to:
From Ancient Greek: (isos, “equal”)
-morphism: the state of having a specified shape or form
Isomorphism may refer to:
- IsomorphismIsomorphismIn abstract algebra, an isomorphism is a mapping between objects that shows a relationship between two properties or operations. If there exists an isomorphism between two structures, the two structures are said to be isomorphic. In a certain sense, isomorphic structures are...
, in mathematics, logic, philosophy, and information theory, a mapping that preserves the structure of the mapped entities - Graph isomorphismGraph isomorphismIn graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H f \colon V \to V \,\!such that any two vertices u and v of G are adjacent in G if and only if ƒ and ƒ are adjacent in H...
, in mathematics, a mapping that preserves the edges and vertices of a graph - Group isomorphismGroup isomorphismIn abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic...
, in mathematics, a mapping that preserves the group structure - Ring isomorphism, in mathematics, a mapping that preserves both the additive and multiplicative structure of a ring
- Isomorphism theoremIsomorphism theoremIn mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and various other algebraic structures...
, in mathematics, theorems that describe the relationship between quotients, homomorphisms, and subobjects - Isomorphism (sociology)Isomorphism (sociology)In sociology, an isomorphism is a similarity of the processes or structure of one organization to those of another, be it the result of imitation or independent development under similar constraints...
, a similarity of the processes or structure of one organization to those of another - Isomorphism (biology)Isomorphism (biology)In biology, an isomorphism is a similarity of form or structure between organisms, generally between organisms with independent ancestries, e.g. after convergent evolution...
, a similarity of form or structure between organisms - Isomorphism (crystallography)Isomorphism (crystallography)In crystallography crystals are described as isomorphous if they are closely similar in shape. Historically crystal shape was defined by measuring the angles between crystal faces with a goniometer...
, a similarity of crystal form - Isomorphism (Gestalt psychology)Isomorphism (Gestalt psychology)In Gestalt psychology, isomorphism refers to a correspondence between a stimulus array and the brain state created by that stimulus. For example, in the phi phenomenon in which a pair of alternating and spatially separated patches of light create the illusion of motion, it is argued that the brain...
, a correspondence between a stimulus array and the brain state created by that stimulus - Cybernetic isomorphism, a recursive property of viable systemsViable System ModelThe viable systems model, or VSM is a model of the organisational structure of any viable or autonomous system. A viable system is any system organised in such a way as to meet the demands of surviving in the changing environment. One of the prime features of systems that survive is that they are...
, as defined by Stafford Beer