Mappings and isometries of compact metric spaces

In the paper it is proved that there exists a continuous surjective mapping F : X -> Y, where X and Y are separable complete metric spaces of transfinite dimension ind less than or equal to alpha(d) is an element of omega(+) boolean OR {infinity} and alpha(r) is an element of omega(+) boolean OR {infinity}, respectively, such that, for each continuous surjective mapping f : X-4 Y, where X and Y are compact metric spaces of transfinite dimension ind less than or equal to alpha(d) and alpha(r), respectively, there are isometries i : X -> X and j : Y -> Y satisfying the relation F circle i = j circle f. This result remains true if we suppose that, for each mapping f : X -> Y, Y coincides with a fixed separable complete metric space Y and that the corresponding mapping j : Y -> Y is the identity. (C) 2017 Elsevier B.V. All rights reserved.