The Current Theory of Analytic Sets

Abstract

In this paper we describe the outlines of the theory of analytic sets from the point of view of recent work on the subject. Our aim is to present the concepts and some of the principal results in a setting useful to workers in analysis, especially those workers not familiar with the field or its current developments. No attempt has been made to include all the results concerning analytic sets—not even in a particular category. There are some excellent monographs(12; 18)as well as chapters in books(2, 8, 9, 15, 17)where the subject is treated extensively. These, however, do not contain the recent results and consider only metric spaces. Our emphasis is on a general topological setting.