Dugundji spaces with distinct dimensions (Q1275990)

According to \textit{V. V. Fedorchuk} [Sov. Math., Dokl. 18, 605-609 (1977); translation from Dokl. Akad. Nauk SSSR 234, 30-33 (1977; Zbl 0375.54026)] for the Dugundji spaces the classical inductive dimensions coincide. He also constructed an example of Dugundji spaces for which the Lebesgue dimension was 1 and the inductive dimension was 2. The author of this paper discusses the problem of the gap between the Lebesgue and inductive dimensions for the Dugundji space.