Weak${}^{\ast }$ dentability index of spaces $C([0,\alpha ])$

Petr Hajek, Gilles Lancien, Antonin Prochazka

We compute the weak${}^{\ast }$-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 general…