mod10lec56 - Regular and Normal spaces

We introduce two new separation properties for topological spaces: regularity and normality. These are part of a list of such properties collectively known as the "Separation Axioms". Given a Haudorff space, regularity is stronger than the Hausdorff property (i.e. a space can be Hausdorff but not regular) and normality is stronger than regularity (i.e. a space can be regular but nor normal). We then give equivalent characterizations of these two properties based on "shrinking" neighbourhoods.