文摘
Given any compact, Hausdorff space K and 1<p<∞, we compute the Szlenk and w⁎-dentability indices of the spaces aa03ed14c811aaec00298964abc5" title="Click to view the MathML source">C(K) and b5bced1b822f" title="Click to view the MathML source">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 aa2228ea3" title="Click to view the MathML source">CB(K)⩽ωξ, then 8c39d7f80a4b5f8c0c2621348a7b6f3" title="Click to view the MathML source">Sz(C(K))=ωξ and aaee2d9e3b0088d90e7e6c84" title="Click to view the MathML source">Dz(C(K))=Sz(Lp(C(K)))=ω1+ξ.