Bifactorial mapping

A mapping of a topological space into a topological space , in which for any covering of the inverse image of any point by sets open in it is possible to select a finite number of sets so that is located inside the image of their union. It is particularly important that the product of any collection of bifactorial mappings is a bifactorial mapping. Bifactorial mappings constitute an extensive class of factorial mappings, but nevertheless preserve the fine topological properties of spaces. Thus, continuous bifactorial -mappings preserve a pointwise-countable base, and a factorial -mapping of a space with a pointwise-countable base onto a space of pointwise-countable type is bifactorial.