Around a Hurewiczʼs formula

Some relevant questions around the Hurewiczʼs formula for the dimension-lowering mappings are under the discussion. In particular, we generalize the notion of a fully closed mapping introduced by V.V. Fedorchuk and find for such new mappings an evaluation formula for the dimension Ind 0 (resp. Ind) of preimages via the dimension Ind 0 (resp. Ind) of images.