Let $C(K)$ be the algebra of continuous functions on Cantor set. Is it possible to prove that $C(K)$ forms an AF-algebra without Bratteli diagram?



The algebra of continuous functions on Cantor set
Sure. Regard $K$ as $\{0,1\}^N$ and let $E\_n$ for $n\in N$ be the functions in $C(K)$ that depend only on the first $n$ components.


