Metrizable images of the Sorgenfrey line

Abstract: We give descriptions of metrizable topological spaces that are images of the Sorgenfrey line under continuous maps of different types (open, closed, quotient and others). To obtain this descriptions, we introduce the notion of a Lusin pi-base, the Sorgenfrey line and the Baire space have Lusin pi-bases, and if a space X has a Lusin pi-base, then for each nonempty Polish space Y, there exists a continuous open map from X onto Y.