On transfinite dimension of topological products (Q1280338)

\textit{R. N. Vinogradov} [Mosc. Univ. Math. Bull. 48, No. 5, 15-17 (1993); translation from Vestn. Mosk. Univ., Ser. I 1993, No. 5, 17-20 (1993; Zbl 0855.54044)] considered the notion of transfinite dimension Id. In contrast to that notion in this paper the definition of transfinite dimension \(\text{Id}^*\) is introduced. This dimension has the property: if \(f\: X\to Y= \prod\{Y_i:i = 1,2,\dots,k\}\) is a continuous, with respect to \(Y\) \(d\)-regular mapping, then \(\text{Id}^* X\leq \text{Id}^*Y_1(+)\dots(+)\text{Id}^*Y_k\).