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Anonymous No. 16228654

Is R^2 isomorphic to C?

Anonymous No. 16228659

Only topologically.

Anonymous No. 16229412

Define "isomorphic". But no.

Anonymous No. 16229518

yes if you define multiplication appropriately

Anonymous No. 16229746

do you mean they are homeomorphic?

Anonymous No. 16229749

they must be since there's a bijection R^2 -> C and (x,y) -> x + iy

Anonymous No. 16229909

They're isomorphic as normed vector spaces over the reals. C is also a ring and a vector space over itself, and R^2 isn't, which makes them not isomorphic in those categories.