  Recently it was highlighted that one-dimensional antiferromagnetic spin
models with frustrated boundary conditions, i.e. periodic boundary conditions
in a ring with an odd number of elements, may show very peculiar behavior.
Indeed the presence of frustrated boundary conditions can destroy the local
magnetic orders presented by the models when different boundary conditions are
taken into account and induce novel phase transitions. Motivated by these
results, we analyze the effects of the introduction of frustrated boundary
conditions on several models supporting (symmetry protected) topological
orders, and compare our results with the ones obtained with different boundary
conditions. None of the topological order phases analyzed are altered by this
change. This observation leads naturally to the conjecture that topological
phases of one-dimensional systems are in general not affected by topological
frustration.
