Anonymous at Tue, 11 Jun 2024 17:28:39 UTC No. 16228659

Only topologically.

Anonymous at Tue, 11 Jun 2024 23:47:25 UTC No. 16229412

Define "isomorphic". But no.

Anonymous at Wed, 12 Jun 2024 01:11:25 UTC No. 16229518

>>16228654
yes if you define multiplication appropriately

Anonymous at Wed, 12 Jun 2024 03:58:53 UTC No. 16229746

>>16228659
do you mean they are homeomorphic?

Anonymous at Wed, 12 Jun 2024 04:01:08 UTC No. 16229749

>>16229746
they must be since there's a bijection R^2 -> C and (x,y) -> x + iy

Anonymous at Wed, 12 Jun 2024 07:15:16 UTC No. 16229909

>>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.