Which Recurrent Sets are Topological Subgroups

We introduce topological de nitions of chain recurrence and shadowing for continuousendomorphisms of topological groups generalizing the relevant concepts formetric spaces. It is proved that in this case the sets of chain recurrent points andchain transitive component of the identity are topological subgroups.

Keywords:

Chain recurrence , Chain component , Shadowing property , Topologicalgroup , Topological entropy