Isomorphism is an algebraic notion, and homeomorphism is a topological notion, so they should not be confused. The notion of homeomorphism is in connection with the notion of a …

Isomorphism is a bijective homomorphism. I see that isomorphism is more than homomorphism, but I don't really understand its power. When we hear about bijection, the first thing that comes …

Can somebody please explain me the difference between linear transformations such as epimorphism, isomorphism, endomorphism or automorphism? I would appreciate if somebody …

There are a few ways to show that a homomorphism of groups is an isomorphism: A homomorphism which is a bijection of sets is an isomorphism. A homomorphism with a two …

The second kind of isomorphism, called isometric isomorphism, preserves all the structure that a Banach space has. Hence, we lose nothing in identifying two spaces that are isometrically …

An isomorphism is a homomorphism that can be reversed; that is, an invertible homomorphism. So a vector space isomorphism is an invertible linear transformation.

We prove that if $f : M \longrightarrow M$ is a surjective $R$ - module homomorphism from $M$ to itself, then $f$ is an isomorphism. It is easy to see that it suffices to prove that $f$ is injective.

The symbol ≅ is used for isomorphism of objects of a category, and in particular for isomorphism of categories (which are objects of CAT). The symbol ≃ is used for equivalence of categories. …

10 What is an isomorphism of sets? I know in general an isomorphism is a structure-preserving bijective map between two algebraic structures. But what algebraic structure does a set have? …

Mar 10, 2019 · Are these two graphs isomorphic? According to Bruce Schneier: "A graph is a network of lines connecting different points. If two graphs are identical except for the names of …