On the estimation of the large inductive dimension of a product of compacta

We prove the analog of Pasynkov's result on finite-dimensionality of topological products for the dimension-like function I defined by S. Iliadis. Let Fj be a normal base on a topological space Xj, j=1,2. Then I(X1×X2,F1⊗F2)≤φ(I(X1,F1),I(X2,F2)), where φ is a recursion relation. As a consequence we get the result on the finite-dimensionality of topological products of compacta for the large inductive dimension.