Abstract
We compute the Szlenk index of the projective tensor product C(K)⊗ˆπC(L) of spaces C(K),C(L) of continuous functions on arbitrary scattered, compact, Hausdorff spaces. In particular, we show that it is simply equal to the maximum of the Szlenk indices of the spaces C(K),C(L). We deduce several results regarding non-isomorphism of C(K)⊗ˆπC(L) and C(M) or C(M)⊗ˆπC(N) for particular choices of K,L,M,N.
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