| Abstrakt: |
For a real-valued sequence ulet τu(R)={x∈R:unx→0modZ}. In Barbieri et al. (Topol Appl 221:534–555, 2017) there were given conditions which imply that τu(R)⊈τv(R). Here we positively answer a question posed in Barbieri et al. (2017) and then in Di Santo et al. (Ric Mat 67:625–655, 2018) showing that these conditions imply that even (τu(R):τu(R)∩τv(R))>ℵ0. Hereby the group cu(R):={x∈R:(unx)n∈Nconverges modZinR}plays an important role. We also present some basic properties of cu(R), the relationship between cu(R)and τu(R)and the connection between these groups and certain totally bounded group topologies on Zand R. |
Full text from SpringerLink