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Hey, up to isomorphism there is only one real n-dimensional vector space.
Up to isomorphism there is only one real-dimensional Slawomir Bialy.
Of course, Slawomir Bialy is always changing, but there is a reasonable
equivalence class, and we call the equivalence class Slawomir Bialy.
There are many different elements of the equivalence class called
the `the n-dimensional real vector space' where equivalence is isomorphism.
This is common usage in mathematics. In any case, it's rude to delete undo
all changes while objecting only to one. — Preceding unsigned comment added by Lost-n-translation (talk • contribs) 16:49, 1 February 2011 (UTC)[reply]
This is true, but of course a vector field is not just a function into another vector space up to isomorphism, it is a mapping into a particular vector space (in mathematics, the tangent space at a point; in physics, it is characterized by a contravariant transformation law). Either way, it's misleading to say that a vector field is a mapping into the n-dimensional real vector space; there is strictly more structure than that. Sławomir Biały (talk) 17:17, 1 February 2011 (UTC)[reply]
