Extension of mappings into spheres and countable decompositions of Tikhonov cubes

In this paper we study several extension problems for maps into spheres, and as a consequence we solve a problem by P. S. Aleksandrov on bicompact condensation. Furthermore, we define a new class of infinite-dimensional spaces, and in investigating them we generalize a classical result of Uryson on Cantor manifolds.
Bibliography: 15 titles.