  In this work, some variation of the concept of attractor are presented,
called attractor, physical attractor and proper attractor. As a result, it is
proved that the phase space of a topologically exact system is a proper
attractor for its inverse and vice versa.
  Furthermore, in definition of physical attractor, one face with systems in
which their phase space attracts all of the open non-empty sets. It is
established that a system is topologically mixing if and only if its phase
space is physical attractor.
  Finally, by appealing to IFSs, we demonstrate some classes of non-trivial
topologically mixing and topologically exact IFSs.
