topological stable rank one and AF-algebra construction on Cantor set

fa.purposeful evaluation – Real rank of $C_0(R)$ Answer

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fa.purposeful evaluation – Real rank of $C_0(R)$

I used to be attempting to compute Real rank of $C_0(mathbb{R} otimes mathbb{Ok}(l^2))$. $mathbb{Ok}$, compact operators algebra, is inductive restrict of matrix algebras. So, $RR(C_0(mathbb{R} otimes mathbb{Ok}(l^2)) = lim_{rightarrow}RR (C_0(mathbb{R} otimes mathbb{M_n})) = C_0(mathbb{R})$. But what the actual rank of $C_0(mathbb{R})$?

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