  A topological measure characterizing symmetry-protected topological phases in
one-dimensional open fermionic systems is proposed. It is built upon the
kinematic approach to the geometric phase of mixed states and facilitates the
extension of the notion of topological phases from zero-temperature to
nonzero-temperature cases. In contrast to a previous finding that topological
properties may not survive above a certain critical temperature, we find that
topological properties of open systems, in the sense of the measure suggested
here, can persist at any finite temperature and disappear only in the
mathematical limit of infinite temperature. Our result is illustrated with two
paradigmatic models of topological matter. The bulk topology at nonzero
temperatures manifested as robust mixed edge state populations is examined via
two figures of merit.
