  In classical Hermitian continuous media, the spectral-flow index of
topological modes is linked to the bulk topology via index theorem. However,
the interface between two bulks is usually non-Hermitian due to the
inhomogeneities of system parameters. We show that the connection between
topological modes and bulk topology still exists despite the non-Hermiticity at
the interface if the system is endowed with PT symmetry. The theoretical
framework developed is applied to the Hall magnetohydrodynamic model to
identify a topological mode called topological Alfv\'{e}n-sound wave in
magnetized plasmas.
