isomorphism class - meaning and definition. What is isomorphism class
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What (who) is isomorphism class - definition

EQUIVALENCE CLASS OF ISOMORPHIC MATHEMATICAL OBJECTS

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)
Isomorphism class         
In mathematics, an isomorphism class is a collection of mathematical objects isomorphic to each other.
Isomorphism (crystallography)         
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TYPE OF CRYSTALS
Law of isomorphism; Law of Isomorphism; Isomorphic series; Isotype (crystallography); Mitscherlich's law of isomorphism
In chemistry isomorphism has meanings both at the level of crystallography and at a molecular level. In crystallography, compounds are isomorphous if their symmetry is the same and their unit cell parameters are similar

Wikipedia

Isomorphism class

In mathematics, an isomorphism class is a collection of mathematical objects isomorphic to each other.

Isomorphism classes are often defined as the exact identity of the elements of the set is considered irrelevant, and the properties of the structure of the mathematical object are studied. Examples of this are ordinals and graphs. However, there are circumstances in which the isomorphism class of an object conceals vital internal information about it; consider these examples:

  • The associative algebras consisting of coquaternions and 2 × 2 real matrices are isomorphic as rings. Yet they appear in different contexts for application (plane mapping and kinematics) so the isomorphism is insufficient to merge the concepts.
  • In homotopy theory, the fundamental group of a space X {\displaystyle X} at a point p {\displaystyle p} , though technically denoted π 1 ( X , p ) {\displaystyle \pi _{1}(X,p)} to emphasize the dependence on the base point, is often written lazily as simply π 1 ( X ) {\displaystyle \pi _{1}(X)} if X {\displaystyle X} is path connected. The reason for this is that the existence of a path between two points allows one to identify loops at one with loops at the other; however, unless π 1 ( X , p ) {\displaystyle \pi _{1}(X,p)} is abelian this isomorphism is non-unique. Furthermore, the classification of covering spaces makes strict reference to particular subgroups of π 1 ( X , p ) {\displaystyle \pi _{1}(X,p)} , specifically distinguishing between isomorphic but conjugate subgroups, and therefore amalgamating the elements of an isomorphism class into a single featureless object seriously decreases the level of detail provided by the theory.