  We show how to generalize the concepts of identifying and classifying
symmetry protected topological phases in 1D to the case of an arbitrary mixed
state. The pure state concepts are reviewed using a concrete spin-1 model. For
the mixed state setup we demonstrate our findings numerically using matrix
product state algorithms. Starting from the ground state and applying various
types of noise sources we find a transient regime where the system is driven
out of equilibrium while retaining its topological properties.
