Separable but not Lindelof examples from Steen and Seebach

We list all the separable but not Lindelof spaces found in Counterexamples in Topology by Steen and Seebach [2]. There are ten such examples. We define the examples and list out the key facts. On these examples, we particularly single out separability and Lindelofness. See here for examples of spaces that are Lindelof but not separable. The disxcussion here is an attempt to locate examples with the opposite properties (separable but not Lindelof). We define each space and describe some of the...