文摘
Given any compact, Hausdorff space K and 1<p<∞, we compute the Szlenk and 14df4ab4290550ad15f22" title="Click to view the MathML source">w⁎-dentability indices of the spaces C(K) and Lp(C(K)). We show that if K is compact, Hausdorff, scattered, CB(K) is the Cantor–Bendixson index of K, and ξ is the minimum ordinal such that CB(K)⩽ωξ, then Sz(C(K))=ωξ and Dz(C(K))=Sz(Lp(C(K)))=ω1+ξ.