TOPOLOGICAL PROPERTIES OF THE SORGENFREY LINE

Abstract

This article investigates the topological properties of the Sorgenfrey line, which is considered one of the fundamental examples in general topology. The Sorgenfrey line is defined as the set of real numbers endowed with a topology generated by the family of half-open intervals [a,b)[a,b][a,b]. The paper analyzes its main properties, including the fact that it is a Hausdorff space and first countable, but not second countable. In addition, it is shown that the Sorgenfrey line is neither separable nor Lindelöf. Special attention is given to its normality and to problems related to its Cartesian product, in particular the non-normality of the Sorgenfrey plane. The obtained results highlight the role of the Sorgenfrey line as a classical counterexample in topology and contribute to a deeper understanding of the relationships between various topological properties.