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arXiv · 0901.0681

Weak$^*$ dentability index of spaces $C([0,α])$

Petr Hajek·Gilles Lancien·Antonin Prochazka
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Abstract

We compute the weak$^*$-dentability index of the spaces $C(K)$ where $K$ is a countable compact space. Namely ${Dz}(C([0,ω^{ω^α}])) = ω^{1+α+1}$, whenever $0\leα<ω_1$. More generally, ${Dz}(C(K))=ω^{1+α+1}$ if $K$ is a scattered compact whose height $η(K)$ satisfies $ω^α<η(K)\leq ω^{α+1}$ with an $α$ countable.

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Petr Hajek, Gilles Lancien, Antonin Prochazka. 2009-01-06. Weak$^*$ dentability index of spaces $C([0,α])$. https://doi.org/10.1016/j.jmaa.2008.11.075

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