On the Asymptotically PT_(-1) Spaces

In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT_(-1) space axe still an asymptotically PT_(-1) space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT_(-1) spaces under particular conditions, which provide some concrete examples of asymptotically PT_(-1) spaces.