Article ID Journal Published Year Pages File Type
4661324 Topology and its Applications 2006 19 Pages PDF
Abstract

In 1969, Arhangel'skiĭ proved that |X|⩽2χ(X)L(X) for every Hausdorff space X. This beautiful inequality solved a nearly fifty-year old question raised by Alexandroff and Urysohn. In this paper we survey a wide range of generalizations and variations of Arhangel'skiĭ's inequality. We also discuss open problems and an important legacy of the theorem: the emergence of the closure method as a fundamental unifying device in cardinal functions.

Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology