Analogs of Cantor manifolds for transfinite dimensions (Q1101728)

The existence of bicompacta, homogeneous in the sense of transfinite small inductive dimension is considered. For every \(\alpha \leq \omega_ 1\) there exists a denumerably dimensional compact \(C^{\alpha}\) such that \(ind_ xC^{\alpha}\geq \alpha\) for every \(x\in C^{\alpha}\). For every \(\alpha <\omega_ 1\) there exists a separable first-countable bicompact \(Y_{\alpha}\) such that \(y_{\alpha}\) is an ind-manifold of the class \(\alpha\), ind \(Y_{\alpha}=\alpha +1\).