An inverse boundary value problem in magnetosphere investigations

Here we study some properties of the dimension $\operatorname{ind}(Y,X)$. The main result is: $\operatorname{ind}(Y,X)\le\operatorname{ind}Y+1$ for all Tychonoff spaces $X$. This enables to prove a generalization of the Uryson inequality. A necessary condition is found for the equality i$\operatorname{ind}(Y,I^\tau)=\operatorname{ind}(Y)$.