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

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

2009-01-06

arxiv.org/abs/0901.0681v1

Journal of Mathematical Analysis and applications, 353 (2009) 239-243

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jmaa.2008.11.075

We compute the weak$^*$-dentability index of the spaces $C(K)$ where $K$ is a countable compact space. Namely ${Dz}(C([0,\omega^{\omega^\alpha}])) = \omega^{1+\alpha+1}$, whenever $0\le\alpha<\omega_1$. More generally, ${Dz}(C(K))=\omega^{1+\alpha+1}$ if $K$ is a scattered compact whose height $\eta(K)$ satisfies $\omega^\alpha<\eta(K)\leq \omega^{\alpha+1}$ with an $\alpha$ countable.

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