The loci \phi=-\pi, \, \pi mark the boundaries of the isotropic chart, and just as in the Schwarschild chart, we tacitly assume that these two loci are identified, so that our putative round spheres are indeed topological spheres.
Just as for the Schwarschild chart, the range of the radial coordinate may be limited if the metric or its inverse blows up for some value(s) of this coordinate.