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Is R^2 isomorphic to C?
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Only topologically.
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Define "isomorphic". But no.
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>>16228654
yes if you define multiplication appropriately
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>>16228659
do you mean they are homeomorphic?
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>>16229746
they must be since there's a bijection R^2 -> C and (x,y) -> x + iy
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>>16228654
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.



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