An example of a topological group

AbstractIn this paper three classes of topological groups are considered: the groups which, in the sense of their topological structure, are Lindelöf P-spaces, and the groups which are o-bounded or strictly o-bounded. In the sense of covering properties these classes are close to σ-compactness.We construct an example of a topological group G which is a Lindelöf P-space but is not strictly o-bounded. The example is generated by a ladder system. We answer some questions of C. Hernandez and M. Tkachenko