Is it true that any 2 vector spaces with the same (infinite) dimension are isomorphic? I think that it is true, since we can build a mapping from $V$ to $\mathbb{F}^{N}$ where the cardinality of $N$ is the dimension of the vector space - where by $\mathbb{F}^{N}$ I mean the subset of the full cartesian product - where each element contains only finite non zero coordinates?
2026-03-26 22:17:56.1774563476
are any two vector spaces with the same (infinite) dimension isomorphic?
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Your argument is quite correct.