Continuous Images of Lusin Sets

Abstract

Abstract.It is the purpose of this note to further clarify the relationship between continuous images of Lusin sets and concentrated sets.We are concerned with subsets of separable metric spaces which have singularity properties such as those discussed in §40 of Kuratowski's Topology [3] (also see [1] for a more complete survey). These are the sets which are "small" in either a Baire categoric sense ("rarified sets" and "always first category" sets) or a measure theoretic sense. We are concerned with the latter type. In particular, consider the following properties of subsets M of a separable metric space X.