Let $F =\mathbb{R}$$F =\mathbb{R}$ or $F=\mathbb{C}$" />. There is a close connection between the algebraic K-groups $K\sb i(F)$" />$K_i(F)$ and the topological K-groups $K^{-i}\sb F(P)$" />$K^{-i}_F(P)$, where P http://latex.mathoverflow.net/png?P$P$ denotes the one-point space. I'm trying to learn this stuff at the moment so I hope someone can fill in the details here (post is community wiki), but I believe the statement is that if you take 2-completions the groups will be isomorphic.