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im trying to get a homeomorphism between a n-dim vector space and R^n that is independent of the basis. (im actually defining a C \infinity structure on V)

since i want a homeomorphism, i know i should define a topology on my vector space, which is the norm, since that would be independent of the basis.

but i cant move forward from there.

any ideas?

btw im fine with a homeom. btw a 1-dim vector space and R since i can write v in V as v1 + v2 + ... + vn where each vi is a vector in 1-dim vector space.

thank you.