On extension of continuous mappings, topological products and retracts

One of the fundamental concepts of the extension theory developed in the works of A. N. Dranishnikov and E. V. Shchepin is the concept of relation of extensiveness, which was introduced by K. Kuratovsky. We describe the behavior of the relation of extensiveness with respect to certain types of subspaces of topological products and spaces, which are the Stone–Cech compactifications of the discrete sums of the Hilbert cube.