On inductive dimensions

We give a definition of dimensional functions $\sigma_f\operatorname{Ind}$, $\sigma_f\operatorname{ind}$ and then prove some factorization theorems for these functions in the class of compact spaces. We show the nonexistence of the universal space in the class of compact spaces $X$ with $\sigma\operatorname{Ind}X\le1$ and $w X\le\varepsilon$.