A Study of Regularity and Normality

Abstract

This paper is a broad overview of the separation axioms, commonly known as the Hausdorff, Regular, and Normal axioms. After a review of basic definitions and lemmas, we proceed to certain examples and theorems dealing with Paracompact and Lindelof spaces. We then progress to metric spaces, separable spaces and countability before we end with several examples of spaces that satisfy certain separation axioms and not others, and the properties that these spaces satisfy.