  We consider certain aspects of cosmological dynamics of a spatially curved
Universe in $f(T)$ gravity. Local analysis allows us to find conditions for
bounces and for static solutions; these conditions appear to be in general less
restrictive than in general relativity. We also provide a global analysis of
the corresponding cosmological dynamics in the cases when bounces and static
configurations exist, by constructing phase diagrams. These diagrams indicate
that the fate of a big contracting Universe is not altered significantly when
bounces become possible, since they appear to be inaccessible by a sufficiently
big Universe.
