Some continuous decompositions of the space En

The main result proved is the following. Let E _f ⁽ⁿ⁾ (n > 1) be a continuous decomposition of E⁽ⁿ⁾ into points and zero-dimensional compact sets . If is compact and dimf(P*) = 0, then the spacef(Eⁿ) can be imbedded in E⁽ⁿ⁺¹⁾.Translated from Matematicheskie Zametki, Vol. 10, No. 3, pp. 315–326, September, 1971.The author wishes to thank L. V. Keldysh for directing this work.