On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
In this paper we study the behavior of the (transfinite) small inductive dimension on finite products of topological spaces. In particular we essentially improve Toulmin’s estimation [T] of for Cartesian products.
Trivially symmetrizable, trivially semi-metrizable and trivially D-completely regular mappings are defined. They are characterized as mappings parallel to symmetrizable, semi-metrizable and D-completely regular spaces correspondently. One shows that trivially D-completely regular mappings, i.e. submappings of fibrewise products of developable mappings coincide (up to homeomorphisms) with submappings of fibrewise products of semi-metrizable mappings.