A diagram of normality properties

Using a diagram as a guide, we present a series of examples of Hausdorff normal spaces that do not have some higher “normality” properties. The examples are to demonstrate that the arrows in the following diagram cannot be reversed. We also give examples showing the properties unrelated by arrows in the diagram are indeed unrelated. For example, there is no arrow connecting perfectly normal and paracompact. We give some examples showing that neither one implies the other. All the examples are...