# Homeomorphism between a 1-dim vector space and R

im trying to get a homeomorphism between a 1-dim vector space and R, but independent of the basis.
Any ideas?

Do you mean homomorphism? Homeomorphisms are maps between topological spaces.

no i meant homeomorphism,
im trying to get a chart (manifolds- C^(/infinity) structure) from V to R
we can though define the norm right and induce a topology on our vector space,
but i still cant see the homeomorphism,
ofcourse the hard thing is that i want it to be independent of the basis, or else, it would've been trivial.

Office_Shredder
Staff Emeritus
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I would be pretty surprised if you could find one that's basis free.

You can't even define the norm without a basis unless you have a basis free definition for a linear isomorphism between V and R.

Hurkyl
Staff Emeritus
Gold Member

Can you give a precise statement of what you mean by "independent of basis"?

yeah sure, i think they mean for whatever choice of bases, we can get the same result.

Hurkyl
Staff Emeritus