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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?

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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.

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  • $\begingroup$ Could you explain a little more? $\endgroup$
    – Peg Leg Jonathan
    Commented Jan 8, 2021 at 19:18
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    $\begingroup$ The $E_n$ are an increasing sequence of subalgefbras with dense union, and for each $n$, $E_n$ is algebra isometric to $\ell_\infty^{2^n}$. $\endgroup$
    – Bill Johnson
    Commented Jan 9, 2021 at 5:23
  • $\begingroup$ It is completely clear now. Thanks. $\endgroup$
    – Peg Leg Jonathan
    Commented Jan 9, 2021 at 6:20

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