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By using K-theory of AF-algebra, the paper characterized the automorphism group on the tensor product of the C(X) and the compact ideal when X is a tottaly disconnected compact Hausdoof space.

利用AF-代数的K-理论，本文还刻划了当X是全不连通的紧致Hausdorff空间时，C（X）与紧算子理想的张量积的自同构群。