If $X_n$ is the bouquet of n circles, then what is $K_0(X_n)$ and $K_1(X_n)$? I am super confused on how to approach this problem, since I've only seen $K_0$, $K_1$ computed for algebras, but I don't understand how the topological space $X_n$ is a C* algebra.
I imagine the solution would involve computing $K_0(\mathbb{R})$, $K_1(\mathbb{R})$ since $X_n$ is the one point compactification of $n$ copies of $\mathbb{R}$. $K_0(\mathbb{R}) = [\mathbb{R}]$ and $K_1(\mathbb{R}) = \frac{GL(\mathbb{R})}{[GL(\mathbb{R}), GL(\mathbb{R})]}$, so would $K_0(X_n) = \Pi_{i=1}^{n}[\mathbb{R}]$, $K_1(X_n) = \Pi_{i=1}^{n}\frac{GL(\mathbb{R})}{[GL(\mathbb{R}), GL(\mathbb{R})]}$?