Linear Algebra/Dimension Characterizes Isomorphism - Wikibooks, open books for an open world
In the prior subsection, after stating the definition of an isomorphism,
we gave some results supporting the intuition that such a map describes
spaces as "the same".
Here we will formalize this intuition.
While two spaces that are isomorphic are not equal, we think of them
as almost equal— as equivalent.
In this subsection
we shall show that the relationship "is isomorphic to" is an equivalence
relation.[1]
https://en.wikibooks.org/wiki/Linear_Algebra/Dimension_Characterizes_Isomorphism
