Definition:Isomorphism Class

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Definition

Algebraic Structures

Let $\struct {S, \circ}$ be an algebraic structure.

Let $\map \II {S, \circ}$ be the class of all algebraic structures which are isomorphic to $S$.


Then $\map \II {S, \circ}$ is known as the isomorphism class of $\struct {S, \circ}$.


Ordered Structures

Let $\struct {S, \preccurlyeq}$ be an ordered structure.

Let $\map \II {S, \preccurlyeq}$ be the class of all ordered structures which are order isomorphic to $S$.


Then $\map \II {S, \preccurlyeq}$ is known as the isomorphism class of $\struct {S, \preccurlyeq}$.