In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are …

Dec 3, 2025 · Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape." …

Consider two subspaces \ (V\) and \ (W\), and suppose there exists an isomorphism mapping one to the other. In this way the two subspaces are related, which we can write as \ (V \sim W\).

Isomorphism, in modern algebra, a one-to-one correspondence (mapping) between two sets that preserves binary relationships between elements of the sets. For example, the set of natural …

Dec 18, 2021 · Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or …

The meaning of ISOMORPHISM is the quality or state of being isomorphic.

Aug 4, 2021 · An isomorphism is a particular type of map, and we often use the symbol $\cong$ to denote that two objects are isomorphic to one another. Two objects are isomorphic there is a $1$ - …

Category theory makes this precise and shifts the emphasis to the 'isomorphism' - the way in which we match up these two objects, to see that they look the same.

Mar 5, 2012 · An isomorphism is a correspondence (relation) between objects or systems of objects expressing the equality of their structures in some sense.

Jul 23, 2025 · In the study of algebraic structures, group isomorphisms and automorphisms play a fundamental role. By defining internal symmetries inside a group (automorphisms) and when two …